Which of these expressions is the simplified form of the expression (StartFraction sine (x) Over 1 minus cosine squared (x) EndFraction) tangent (StartFraction x Over 2 EndFraction) ?

Answers

Answer 1

Answer:

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]

Step-by-step explanation:

Given

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]

Required

Simplify

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]

---------------------------------------------------------------------------------------------------

Considering the denominator of the first bracket

[tex]1 - cos^2x[/tex]

This can be rewritten using different of two squares as follows:

[tex](1 - cosx)(1 + cosx)[/tex]

So, [tex]1 - cos^2x[/tex] can be replaced with [tex](1 - cosx)(1 + cosx)[/tex] in the given expression.

Also, from trigonometry identity

[tex]tan\frac{x}{2} = \frac{1 - cos x}{sin x}[/tex]

So, [tex]tan\frac{x}{2}[/tex] can be replaced with [tex]\frac{1 - cos x}{sin x}[/tex] in the given expression

---------------------------------------------------------------------------------------------------

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex] becomes

[tex](\frac{sinx}{(1-cosx)(1+cosx)}) * \frac{1 - cos x}{sin x}[/tex]

[tex](\frac{sinx * (1 - cos x)}{(1-cosx)(1+cosx) * sin x})[/tex]

Cancel out similar expressions

[tex]\frac{1}{1+cosx}[/tex]

The expression cannot be further simplified.

Hence:

[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]

Answer 2

The simplified form of the expression :

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]

We have some trigonometric formula as:

[tex]sin2x=2sinx= cosx\\2cos^{2} x=1+cos2x[/tex]

We have the expression

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} \\=\frac{sinx}{sin^{2} x} .tan\frac{x}{2} \\=\frac{1}{sin x} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .\frac{sin\frac{x}{2}}{cos\frac{x}{2}} \\=\frac{1}{2cos^{2} \frac{x}{2}}\\=\frac{1}{1+cos{x} }[/tex]

Therefore, the simplified form of the expression is:

[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]

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Related Questions

look at picture
look at picture​

Answers

Answer:

point ??????? I think not sure

HELPPPP PLS ASAPPPPP EASY

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Answer:

on what

Step-by-step explanation:

??????

Answer:

What do you need help with?

Step-by-step explanation:

Upload a picture

175 miles at a speed of 25 miles per hour?

Answers

Answer:

That would take you 7 hours to get to your location.

175 / 25 = 7 so yes it is correct!

how do you solve for x
-3x-6y=0

Answers

Answer:

x = 2y

Step-by-step explanation:

Simplifying

3x + -6y = 0

Solving

3x + -6y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6y' to each side of the equation.

3x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0

3x + 0 = 0 + 6y

3x = 0 + 6y

Remove the zero:

3x = 6y

Divide each side by '3'.

x = 2y

Simplifying

x = 2y

Kai is making a chessboard using pieces of wood that measure 1 square inch.
When he finishes, the chessboard will have an area of 64 square inches.
How many pieces of wood should he put along each side?
A cube has a volume of 125 cubic inches. What is the length of each edge?

Answers

Answer:

The correct option will be:   c.  8 pieces of wood.Step-by-step

what is /4 of 3/4 =
What is 1/4 of 3/4

Answers

Answer:

3/16

Step-by-step explanation:

1/4 of 3/4 is just another way of saying (1/4)*(3/4). When multiplying fractions, you must multiply the numerators and denominators to get the product so the numerator of the products is 1*3 and the denominator is 4*4 to get:

3/16

Answer:

3/16

Step-by-step explanation:

1/4 of 3/4

= 1/4 × 3/4

you multipy the numerators together and then multiply both denominators

ie. 1×3 divided by 4×4

= 3/16

Which two options describe the standard deviation?


The variance square


The extreme distance from the mean expected from the data points


The square root of the variance.


The average distance from the mean expected of the data.

Answers

Answer:

The square root of the variance.

The average distance from the mean expected of the data.

Step-by-step explanation:

Standard deviation is a measure of dispersal. It determines the average distance from the mean expected of the data.

Variance is also related to the standard deviationIt is the square root of the variance. The dispersion or variation of a set of values away from the mean is the standard deviation.

       

                Standard deviation = [tex]\sqrt{variance}[/tex]

Rewrite 3^-7 using a positive exponent.

Answers

Answer: 1/3^7

Step-by-step explanation:

I need help with Number 7 please!!!

Answers

Answer:

8.06 ft or [tex]\sqrt{65}[/tex]  ft

Step-by-step explanation:

Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex]  ft per side. This can be approximated to 8.06 ft.

8.06 ft
Mark me as the brainliest please I spent 25 hours working on this. Thank you very much little boo. You are so segsy. Go get some Bob pics from mother’s boyfriend. 8.06 under your di37 hole

Kyle plans to estimate the area of the figure below by identifying the full and partial squares that make up the figure.
If Kyle uses the strategy, which statement best describes the figure?
O 20 full squares and 8 partial squares
0 24 full squares and 12 partial squares
0 36 full squares and 12 partial squares
O 40 full squares and 8 partial squares

Answers

Answer:

The answer is one hundred percent D

Step-by-step explanation:

Hi

Answer:

D

Step-by-step explanation:

How many 1-inch cubes fill one row of the carton?

Answers

Answer: 5 because it has 5 space left

Answer:

5

Step-by-step explanation:

i did this on i-ready and got it right Good luck!

the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat​

Answers

Answer:

450

Step-by-step explanation:

First we have to find the discount

20% of 1500 = 300

if you search up 20 x 1500/100, it would say 300

you can do that same equation in your maths book, and also by canceling out

10% vat tax

so 10% of 1500 = 150

since it is tax, we have to add it to our discount

300 + 150 = 450

450 is the answer

Y-intercept:(??,??)
X-intercept: (??,??)

Answers

Answer:

the y-intercept is 2.5 or 2 and 1/2

the x-intercept is 3.5 or 3 and 1/5

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Y- 3 and X-4 Is the intercepts

How many pounds are in 80 kilograms?

Answers

Answer:

176.37 pounds are in 80 kilograms

Step-by-step explanation:

The kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.

A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms.

Geometric Sequence♡

5, -2, 4/5

the common ratio was 2/5

find the 10th term​

Answers

If this helped please mark brainliest:)

9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days

Answers

Answer:

0.5818

Step-by-step explanation:

Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.

Answer:

The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score[/tex]

Given that:

[tex]\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67[/tex]

Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818

Armando and Mikayla have a new grandson. How much money should they invest now so that he
will have $80,000 for his college education in 18 years? The money is invested at 8% compounded
annually

Answers

9514 1404 393

Answer:

  $20,020

Step-by-step explanation:

The future value formula is helpful.

  FV = P(1 +r)^t

  $80,000 = P(1.08^18) = 3.9960195P

  P = $80,000/3.9960195 = $20,019.92

They should invest about $20,020 now.

HELP PLEASEEEE! suppose the average wait time for a sandwich at a local deli is 5 min with a standard deviation of 3 min. Is it unusual to get a sandwich in only 12 minutes?

A. Yes because 12 min is more than two standard deviations below the mean.

B. No, because 12 min is less than two standard deviations above the mean.

C. No, because 12 min is more then two standard deviations above the mean.

D. Yes because 12 min is more than two standard deviations above the mean.

Answers

Answer:

D

Step-by-step explanation:

Here, we want to state if it is unusual or not get a sandwich in 12 minutes given the mean time and the standard deviation.

The answer here is that it is unusual.

The reason why it is unusual is because, two standard deviations above the mean in this case will be 5 + 3 + 3 = 11

Looking at the value given which is 12, we can see that this value is actually greater than the value which is 2 standard deviations above the mean.

What we are saying here is that 12 is greater than two standard deviation above the mean which is valued at 11

Morgan born is paid $11.20 an hour for a 40-hour week.Her estimated benefits are 33% of her wages.What is value of her total yearly employee benefits?

Answers

Answer:

Как ты это делаешь

Step-by-step explanation:

In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?

Answers

Answer:

Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.

Step-by-step explanation:

this is correct...

trust me :)

The sign is positive because it represents a quantity of something, in this case, months.

Callie has 4 months to pay off the bill.

The rational number is +4.

What is the rational number?

A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

The sign is positive because it represents a quantity of something, in this case, months.

To learn more about the rational number visit:

https://brainly.com/question/1535013

#SPJ2

7th grade math help me plzzz

Answers

Where’s the question ??

Answer:

-7 minus 9 = -16

-3-(-10) =7

8-12=-4

4-(-5)=9

Step-by-step explanation:

im in 7th grade on edginuity got it all right

For a certain product we obtained a regression line equation Y = 10 - 0.8 X, where X is price (in $) and Y is sales (in $1,000). The slope of the line (- 0.8) represents:___---.
A. If the price were $10, expected sales would be $8,000.B. If the price were zero, expected sales would $800.C. If the price increases by $1, sales will decrease by $800, on average.D. Sales are maximized when the price is $0.8.
E. None of the other answers are correct.

Answers

Answer:

C. If the price increases by $1, sales will decrease by $800, on average

Step-by-step explanation:

Slope of regression equation represents the increase/decrease in dependent variable Y due to unit change in independent variable X. Here, independent variable is X is price and dependent variable Y is sales. The slope negative sign represent decrease in dependent variable due to unit increase in independent variable. Sales is given in ($1000) So, (0.8*1000)=800. It means that due to unit dollar increase in price the sales will decrease by $800. Thus, If the price increases by $1, sales will decrease by $800, on average is the correct interpretation.


2. Use prime factorization to find the
LCM of 30 and 75.

Answers

Answer:

150 is the LCM for 30 and 75

Round 24,837,618 to the ten thousands place. I’m on math college so I need help on this problem!

Answers

Answer:

24,840,000

Step-by-step explanation:

Round up of numbers includes rounding them up to a given place value.

We are asked to round 24,837,618 to the ten thousands place.

The ten thousands place is the place where the number 3 in the number is located.

The number after 3 = 7 is a number above 5. Hence, we add 1 to 3, making it 4

Therefore, 24,837,618 to the ten thousands place is 24,840,000

Use rounding to estimate the product of 5,555 and 4,444 round both numbers to the nearest thousand to find answer

Answers

Step-by-step explanation:

Given that the first number is

5,555 and

the second number is 4,444

the product of 5,555 and4,444= 24686420

to the nearest thousand 5,555= 6000

to the nearest thousand 4,444= 5000

Therefore the product of 6000 and 5000 is

=6000x5000

=30000000

Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. Use the information in Example 3 of Section 3.1 to determine the appropriate age of a piece of burned wood, if it was found that 88% of the C-14 found in living trees of the same type had decayed. (Round your answer to the nearest hundred years.) years

Answers

Answer:

The age of the wood is [tex] t =  17527.5 \  years [/tex]

Step-by-step explanation:

   From the question we are told that 88% of  of the C-14 found in living trees of the same type had decayed , this means that the proportion of C-14 that is remaining is mathematically evaluated as

    [tex]  1 - 0.88 = 0.12[/tex]

Hence

[tex] N = 0.12N_o[/tex]

Here  N represents the remaining C-14 while [tex]N_o[/tex] is the original  amount of  C-14

Generally the half life of C-14 is  [tex]h =  5730 \  years[/tex]

Generally from the formula of radioactive decay

       [tex]N  =  N_o  *  2^{-\frac{t}{h} }[/tex]

=>    [tex]0.12N_o =  N_o  *  2^{-\frac{t}{5730} }[/tex]

=>    [tex]0.12  =    2^{-\frac{t}{5730} }[/tex]

taking the natural log of both sides

=>  [tex] ln [0.12]  =   ln[ 2^{-\frac{t}{5730} }][/tex]

=>  [tex] ln [0.12]  =  -\frac{t}{5730}ln(2) [/tex]

=>   [tex] t =  17527.5 \  years [/tex]

The appropriate age of burned wood will be "17527.5 years".

Radioactive decay

According to the question,

The proportion of C-14 = 1 - 0.88

                                      = 0.12

then,

N = 0.12 N₀

Now,

The half-life of C-14 will be:

h = 5730 years

By using Radioactive decay formula, we get

→      N = N₀ × [tex](2)^{-\frac{t}{h} }[/tex]

By substituting the values,

0.12N₀ = N₀ × [tex](2)^{-\frac{t}{5730} }[/tex]

   0.12 = [tex]2^{-\frac{t}{5730} }[/tex]

By taking "log" both sides,

ln[0.12] = ln[[tex]2^{-\frac{t}{5730} }[/tex]]

ln[0.12] = -[tex]\frac{t}{5730 \ ln(2)}[/tex]

hence,

The age will be:

         t = 17527.5 years

Thus the above response is correct.

Find out more information about radioactive decay here:

https://brainly.com/question/1236735

Jason delivers newspapers on Saturdays and Sundays only. Each newspaper weighs about 1 pound 5 ounces. If he delivers 15 newspapers each day, how much do the two days' worth of newspapers weigh in pounds and ounces?

Answers

Answer:

39pounds 6oz

Step-by-step explanation:

15x2=30

1x30=30pounds

5x30=150oz

30p+150oz=39.37500

37500p=6oz

39pounds and 6 oz

Can any one help me?

Answers

8x + 5 + 4x - 17 = 180

12x - 12 = 180

12x = 192

x = 16

The value of x is 16.
16
Explanation idkkkkk1

Which equation expresses d in terms of t and a?

Answers

Answer:

Option D

Step-by-step explanation:

I got it right

A family is purchasing 17 tickets for a downtown walking tour. Adult tickets are $10, child tickets are $7, and senior tickets are $8.50. The total

cost of the tickets is $141.50, and they are purchasing 2 more senior tickets than adult tickets.

Create and solve a system of linear equations to represent this situation. Then select the true statement.


А. The solution to this system is nonviable because it results in a fractional number of tickets.

B. The solution to this system is no viable because it results in a negative number of tickets.

C. The solution to this system is viable.

D. The solution to this system is nonviable because it results in a fractional amount of money.

Answers

Answer:

А. The solution to this system is nonviable because it results in a fractional number of tickets.

Step-by-step explanation:

Let x represent the number of adult tickets, y represent the number of child ticket and z represent the number of senior ticket.

Since the number of purchased ticket is 17, hence:

x + y + z = 17         (1)

The total cost of tickets is $141.50, hence:

10x + 7y + 8.5z = 141.5       (2)

they are purchasing 2 more senior tickets than adult tickets, therefore:

x = z + 2        (3)

Solving equation 1 2 and 3 simultaneously gives:

x =17/3, y = 23/3, z = 11/3

Therefore the solution to this system is nonviable because it results in a fractional number of tickets.

Answer:

А.The solution to this system is nonviable because it results in a fractional number of tickets

Step-by-step explanation:

took the test on edmentum and got it correct

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It takes Daphne 25 minutes to assemble a model plane. During her work day Daphne takes 30 minutes for lunch and one 15 minute break. Which inequality could Daphne use to determine the number of model planesshe can assemble in her 8 hour work day?25p - 458 In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.P (win) = A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.Answer: $A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.Answer: $ Here is the last one. is techonalygy harmful or useful A radio station requires DJs to play commercials for every 8 songs they play. What is the unit rate of songs to commercials. any one know the answer plz i will give brainlyest Find the slope of the line Solve for g.2(g - 13) = 12g -4 (2x + 13) + 3x = 80How do you solve this out and get the answer [Same investments as the prior question] Suppose two local start-ups are raising funding by issuing shares of equity at $10,000 per share. One start-up is a whiskey distillery; the other is a beer brewery. You estimate the expected returns on your investment to be 50% over five years in both cases. You also believe that the likelihood of being paid out $20,000 per share is greater with the distillery than with the brewery. Suppose now that you hold a portfolio of many other risky assets, and that this would be your N 1 investment. Which investment do you prefer to make, the distillery or the brewery Which decimal represents86100?0.040.140.160.86 Describe a time when you discovered or experienced something that made you see the world differently. How did it cause you to change? which of the following projects would you use as a dictionary entry OMG PLEASE HELP MEEE!!!! Which is not considered a Disney Princess a) Princess Leia b) Princess Cinderella c) Princess Auroa d) Princess Jasmine Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.52. Using the empirical rule, what percentage of American women have shoe sizes that are at least 12.6?Please do not round your answer. Number 10 plzz??????? The three basic structures for bacteria are:[mark all correct answers]a. bacillusb. anaerobesc. aerobesd. spirillumO e. coccus What is created during the design phase of ADDIE as a vehicle for feedback before moving on to the next stage?A) ThesisB) StoryboardC) PrototypeD) Internship A number line going from negative 3 to positive 5. An open circle is at 1.5. Everything to the right of the circle is shaded. Which symbol completes the inequality represented on the graph? z _____ 1.5 > Greater-than-or-equal-to < Less-than-or-equal-to