Mathematics High School

d/d{cosec^-1(1+x²/2x)} is equal to​

D/d{cosec^-1(1+x/2x)} Is Equal To

Answers

Answer 1

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)[/tex]

Let assume that

[tex]\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)[/tex]

We know,

[tex]\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}[/tex]

So, using this, we get

[tex]\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)[/tex]

Now, we use Method of Substitution, So we substitute

[tex] \red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}[/tex]

So, above expression can be rewritten as

[tex]\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)[/tex]

[tex]\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)[/tex]

[tex]\rm\implies \:y = 2z[/tex]

[tex]\bf\implies \:y = 2 {tan}^{ - 1}x[/tex]

So,

[tex]\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x[/tex]

Thus,

[tex]\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)[/tex]

[tex]\rm \:  =  \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)[/tex]

[tex]\rm \:  =  \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)[/tex]

[tex]\rm \:  =  \: 2 \times \dfrac{1}{1 + {x}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2}{1 + {x}^{2} } [/tex]

Hence,

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}[/tex]

Hence, Option (d) is correct.

Related Questions

help with the top one please?

Answers

Answer:

30 pages per hour.

Step-by-step explanation:

Okay so they read 1 1/2 pages per hour right. And you need 20/20 to make 1 hour right. So all you have to do is multiply 1 1/2 by 20 and you got your answer.

What are the correct answers to this geometry problem?

Answers

Answer:

3. HI

4. GI  JH  JG

-If you thought that I was helpful, go ahead and give me the brainliest answer!

PLEASE HELP ANSWER THIS QUESTION
(ILL GIVE BRAINLIEST TO THE BEST ANSWER TOO)
In Earth's southern hemisphere, the summer season is from December to March and winter is from June to September. The table shows the highest temperatures recorded at the South Pole for three different months.

Graph model:
South Pole Temperatures
Month Highest temperature (°F)
January 6
June –24
November –2

Each month's highest recorded temperature is plotted on the number line.

4. Which month had the coldest of the three temperatures? Explain.

Answers

#4

June is the most coldest.

How?

Mention the temperatures

January=+6°CJune=-24°CNovember=-2°C

Lowest is the coldest .(June is the coldest month)

Answer:

January = 6°F

June = -24°F

November = -2°F

By the above given observation we can say that June is the coldest as it has the lowest temperature in all.

In the year 2015 Emily was three times as old asKaitlin. By the year 2021 Kaitlin will be half asold as Emily will be. How old was Emily on theyear 2000?

Answers

In 2000 Emily was 9 years old.

Given that in the year 2015 Emily was three times as old as Kaitlin while by the year 2021 Kaitlin will be half as old as Emily will be, to determine how old was Emily on the year 2000 the following calculation must be performed:

2015 = E = 3K 2021 = E = 2K  24 /// 8 --- 30 /// 14 18 /// 6 --- 24 /// 12 18/6 = 3 24/12 = 2 2015 = Emily was 24 years old 24 - (2015 - 2000) = X 24 - 15 = X 9 = X

Therefore, in 2000 Emily was 9 years old.

Learn more in https://brainly.com/question/20025195

What is the missing integer?

Answers

Answer:

The answer would be negative 1

Answer:

-1+3=2

Step-by-step explanation:

answer:-1

Planes T and X are parallel. Plane T contains like a. plane x contains line b

Answers

Answer:

c lines

Step-by-step explanation:

how do you solve this and what is the answer?

y-3=5/2(x-3)

Answers

I hope this is right

pls help! reporting fake answers!! :)

Answers

Answer:

for #1... 5 cups of yellow paint

Step-by-step explanation:

If 2 blue need ten yellow then 1 blue would need half what 2 needs so 5 yellow for 1 blue

find the vaalue of x 3x+ y+ 2z= -10 x+5y+2y+2z= -12 -2x+3y= -1

Answers

x+7y+2z=−12

I'm not 100% sure though

What do you add to
2 1/5 to make 5

Answers

Answer:

Another 2 1/5

Step-by-step explanation:

2.5 + 2.5 = 5.0 (You don't have to put the .0)

Another example would be:

5.5 + 5.5 = 11.0 (Again, you do not have to put the .0)

- Hope this helps (:

Is the following a function?
{(1, -2), (-2, 0), (-1, 2), (1,3)}

Answers

it is not a function. A function is a relation in which no two ordered pairs have the same input (or x-values) and different outputs (y-values).

You need to determine whether every first element (or input) correspond with EXACTLY ONE second element (or output).

in this case, the input value of 1 goes with two output values, -2 and 3.  

It only takes one input value to associate with more than one output value to be invalid as a function.

Therefore, the given relation is not a function.

convert 32.6 mph into cm per seconds

Answers

Answer:

1457.35

Step-by-step explanation:

If 1/3 is equivalent to 33 1/3%, what percent is equivalent to 2/3?

A: 33 2/3%
B: 150%
C: 66 2/3%
D: 65%

Answers

Answer:

   C    66 2/3%

Step-by-step explanation:

1/3 =  33 1/3%  

1/3 = 33 1/3 ∙ 1/100             % means 1/100

1/3 = 100/3 ∙ 1/100                33 1/3=    (33∙3+1)/3=100/3

1/3 = 100/300                         Reduce

1/3 = 1/3   Check    so  

1/3 = 33 1/3%

Now     2/3=?%

We know that     2/( 3) =  N ∙ 1/100      meaning of percent (%)

                            2/3 = N/100              

                          200 = 3N

                           200/3 = N

                            66.66 =N      

 Therefore      2/3 = 66 2/3  %            

Sally paid $3.50 for 7 apples.

Answers

Answer:

each apple costs 50 cents

Step-by-step explanation:

3.50/7=0.50

Why did sally buy 7 apples

On the last algebra test M students scored x on the test and N students
scored y. What does the following expression represent?
Mc+Ny
M+N

Answers

Answer: Y=35x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mx + Ny represents the total score of M + N students.

decrease 475.29 by 2.1%

Answers

The answer is 465.30891

Please help me with this PLEASE

Answers

Answer:

The slope is 5/3

Step-by-step explanation:

-3 over to 0 is 3, so you get the run.

-2 up to 3 is 5, so you get the rise.

Slope is rise over run, which gives the answer of 5/3.

Good luck!

Felix buys 5 kilograms of corn tortilla chips. How much does he spend?

Answers

Answer:

$10

Step-by-step explanation:

5 times $2 equals $10

Answer:

$10

Step-by-step explanation:

Each kg of corn tortilla chips: $2

5 kgs of corn tortilla chips: 5*2

= $10

Hope this helps and have a wonderful time ahead at Brainly! :D

what is the slope of a line b perpendicular to line a with equation y=7x-9

Answers

Answer:

The slope of line b would be -1/7.

Step-by-step explanation:

This happens because if you have the slope of any line and are trying to find the perpendicular line to said line, the slope of the perpendicular line will always be the opposite reciprocal of the original slope.

Then, all you need to do is find some points and graph the lines.

y-6=-4(x+4) show steps.

Answers

Answer:

y = -4x - 10

Step-by-step explanation:

y-6=-4(x+4)

1: distributive property

y-6= -4x - 16

2: add 6 both sides

y = -4x - 10

which angles are alternate interior angles​

Answers

Answer:

2nd

Step-by-step explanation:because

the width of a rectangle is 3 inches less than its length the perimeter of the rectangle is 26 inches what is the width of the rectangle

Answers

Answer:

5

Step-by-step explanation:

W = x

L = x + 3

P = 2W + 2L

26 = 2(x) + 2(x + 3)

26 = 2x + 2x + 6

26 = 4x + 6

26 - 6 = 4x

20 = 4x

x = 5

The pet boarder keeps a dog to cat ratio of 5:2. If the boarder has room for 98 animals, then how many of then can be dogs?

Answers

for every 5 dogs, there are 2 cats.
if there is room for 98 animals, there would be 70/98
so 5 for every 7= x/98

If you scale up the ratio on the left, what will you get for the unknown quantity on the right? $155 $465

-------- = --------------

20 hours ?


A. 10 HOURS

B. 40 HOURS

C. 60 HOURS

D. 100 HOURS

Answers

Answer:

60 minute equals to 1 hour

guy pls help me!!!!!

Answers

it’s 63 degrees because the square is 90 degrees the other one is 27 degrees so add them and subtract from 180 because there is 180 degrees in a triangle

plsssssssssssssss helppppppppppppppppppppp

Answers

Answer:

It would be (2,8)

Step-by-step explanation:

x goes up by 1 and y goes up by 2

Plz Help! A B C or D. I already pressed one but I dont know which one​

Answers

Answer:

D. y = 50

Step-by-step explanation:

Both of the points have same y- coordinate of 50.

It means the slope is zero and the line is parallel to the x- axis.

The line has equation:

y = 50

Correct choice is D

Slope

m=50-50/25+25m=0

Points are parallel

Equation

y=50

use the distibutive property to find the product
1/5 x 5 10/11​

Answers

Answer:

1/2/11

Step-by-step explanation:

1/5×5/10/11=1/5×65/11

=13/11

=1/2/11

y= tan(X-π/5) tìm tập xác định của hs

Answers

Answer:

?

Step-by-step explanation:

Scott has 18 3/4 gallons of gas in his tank. If he uses 3/50 gallons of gas per mile he drives how many miles can he drive before his tank is empty.? Pls help!

Answers

Answer:

Step-by-step explanation:

I’m sorry that i can’t fully help and that i answered it wrong twice i also got stuck. I hope someone else helps you and that you get an a

18 3/4 as an improper fraction is 75/4.

75/4 can be re-written as 1875/100 (multiply both sides by 25)

3/50 can be re-written as 6/100 (multiply both sides by 2)

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