Answers
Step-by-step explanation:
[tex]\bf L.H.S = \tt \dfrac{sec\: \theta + tan \: \theta - 1}{tan \: \theta - sec \: \theta + 1} \\ \\ [/tex]
[tex]: \implies \tt \dfrac{\frac{1}{cos \: \theta} + \frac{sin \: \theta}{cos \: \theta} - 1}{ \frac{sin \: \theta}{cos \: \theta} - \frac{1}{cos \: \theta} + 1 } \: = \dfrac{1 + sin \: \theta - cos \: \theta}{sin \: \theta + cos \: \theta} \\ \\ [/tex]
[tex]: \implies \tt\dfrac{ sin \: \theta - (cos \: \theta - 1)}{sin \: \theta + (cos \: \theta - 1)} \: \times \: \dfrac{ sin \: \theta - (cos \: \theta - 1)}{sin \: \theta - (cos \: \theta - 1)} \\ \\ [/tex]
[tex]: \implies \tt\dfrac{ sin^{2} \: \theta + cos^{2} \: \theta + 1 - 2 \: cos \: \theta - 2 \: sin \: \theta \: (cos \: \theta - 1)}{sin^{2} \: \theta - (cos \: \theta - 1)^{2} } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{1 + 1 - 2 \: cos \: \theta - 2 \: sin \: \theta \: cos \: \theta + 2 \: sin \: \theta}{sin^{2} \: \theta + cos^{2} \: \theta - 1 + 2 \: cos \: \theta } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{2 - 2 \: cos \: \theta - 2 \: sin \: \theta \: cos \: \theta + 2 \: sin \: \theta}{sin^{2} \: \theta + cos^{2} \: \theta - sin^{2} \: \theta - cos^{2} \: \theta + 2 \: cos \: \theta } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{2 (1 - \: cos \: \theta )- 2 \: sin \: \theta (1 - \: cos \: \theta)}{ 2 \: cos \: \theta - 2 \: cos^{2} \: \theta} \\ \\[/tex]
[tex]: \implies \tt\dfrac{(2 + 2 \: sin \: \theta) \: \cancel{(1 - cos\: \theta)}}{2 \: cos \: \theta \: \cancel{(1 - cos \: \theta)}} \: = \: \dfrac{1 + sin \: \theta}{cos \: \theta} \\ \\[/tex]
[tex]: \implies\tt\dfrac{1 + sin \: \theta}{cos \: \theta} \: \times \: \dfrac{1 - sin \: \theta}{1 - sin \: \theta} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{1 + sin^{2} \: \theta}{cos \: (1 - sin \: \theta)} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{cos^{2} \: \theta}{cos \: \theta (1 - sin \: \theta)} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{cos \: \theta}{1 - sin \: \theta} \: = \: \bf{ R.H.S}\\ \\ [/tex]
[tex]\huge\bigstar \:\underline{\red{\sf Hence, Proved}} \: \bigstar \\ [/tex]
Related Questions
HELP ME PLEASE!! Find R and theta with the coordinates (-3,7).
Answers
Answer:
Since r is the distance from the origin to (x,y), it is the magnitude r=√x2+y2. Alternatively, from the equation (1), one can calculate directly that x2+y2=r2cos2θ+r2sin2θ=r2(cos2θ+sin2θ)=r2.
Step-by-step explanation:
I need help with this
Answers
Answer:
Quadrilateral, parallelogram, rectangle
Step-by-step explanation:
i believe those are the right ones
Ciana worked 5 hours on Saturday and
6.5 hours on Sunday. If she earns $7.00
an hour how much did she earn?
Answers
Answer: $80.50
Step-by-step explanation:
intergers: -6+3 plz help me and plz show how you figured it out i can’t
Answers
Answer:
-3
this diagram might help you ( ◜‿◝ )♡
Answer:
Question : -6 + 3 =?
Answer : -3
24 divided by 9 simplified
Answers
Answer:
8/3
Step-by-step explanation:
Courtney and Malik are buying a rug to fit in a
50-square-foot space, Which rug should they
purchase? Explain.
$99 Rug Sale!
7 ft x 7 ft
8 ft diameter
6 ft x 8ft
Rug Emporium has your floors covered.
Answers
Answer:
I think its 7x7 because it equals to 49 and its the closest to 50 and the rug would fit better than 6x 8 1/2=51 becuase 49 is smaller and would fit better.
Step-by-step explanation:
The area of a 2D form is the amount of space within its perimeter. The correct option is B, 8ft diameter.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Since Courtney and Malik want the rug to fit in an area of 50-square-foot space. Therefore, we need to first calculate the area of the given rugs, and then choose the one that can completely cover the area.
7 ft x 7 ft → Area = 7 ft x 7 ft = 49 ft²8 ft diameter → Area = (π/4)×Diameter² = (π/4)×(8ft²) = 50.2654 ft² 6 ft x 8ft → Area = 6 ft x 8ft = 48 ft²Now, as it can be seen that the only rug that can completely cover the 50-square-foot area is the one that has a diameter of 8 ft.
Hence, the correct option is B, 8ft diameter.
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Which term has an expression with a base of 8
Answers
Answer:
8^4
Step-by-step explanation:
A 'base' is a number with an exponent.
The expression [tex]8^4[/tex] has the base 8.
We need to find which of the given term has an expression with a base of 8.
What is base of an expression?A numerical system's number basis, or base for short, informs us of the particular or distinctive symbols and notations it employs to express a value. The number used to construct a power with an exponent, such as the 3 in 3², is known as the base.
In the expression [tex]8^4[/tex], 8 is the base and 4 is the power or exponent.
Therefore, the expression [tex]8^4[/tex] has the base 8.
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Angle A equals 30 degrees side a equals 7 and side b equals 12
Answers
Answer:
to make chocolate milk, the lunch lady uses 4 cups of white milk for each cup of chocolate milk
Step-by-step explanation:
5t-9=-3t+7. I need help this is equations variables both sides
Answers
Answer:
t = 8
Step-by-step explanation:
5t - 3t - 9 = 7
5t - 3t = 7 + 9
2t = 7+ 9
2t = 16 <- divide
Answer"
t = 8
Hope this helped
Brainliest is appreciated/
Hey there!☺
[tex]Answer:\boxed{t=2}[/tex]
[tex]Explanation:[/tex]
[tex]5t-9=-3t+7[/tex]
Let's start by adding 3t to both sides of the equation.
[tex]5t-9+3t=-3t+7+3t\\8t-9=7[/tex]
Now let's add 9 to both sides of the equation.
[tex]8t-9+9=7+9\\8t=16[/tex]
Now let's divide both sides by 8.
[tex]\frac{8t}{8} =\frac{16}{8}[/tex]
Now let's simplify 16/8.
[tex]16/8=2[/tex]
[tex]t=2[/tex]
Hope this helps!
Angle XYZ = 2X ° and angle PQR = (8X -20)° if angle XYZ and angle PQR or supplementary find the measure of each angle angle XYZ = ?
Answers
Answer:
angle XYZ = 40°
Step-by-step explanation:
given,
angle XYZ = 2x°
angle PQR = (8x-20)°
now,
2x+8x-20° = 180°{being supplementary angle}
or, 10x - 20° = 180°
or, 10x = 180°+20°
or, x = 200°/10
or, x = 20°
again,
angle XYZ = 2x°
= 2× 20°
= 40°
4 y = 38 - 0.5 ( 6 y - 22 )
Answers
4y+3y=38-11-3y+3y
7y=27
7y/7=27/7
Y=27/7
1.5
For use after Le
Divide, if possible.
1. 3+ (-1)
Answers
Answer:
2 i think it's 2 now sure
Step-by-step explanation:
ummmmmmmmmmmmmmm
Solve x − 2y = 3 for x.
Answers
Answer:
[tex]x=2y+3[/tex]
Step-by-step explanation:
So we have the equation:
[tex]x-2y=3[/tex]
And we want to solve for x. In other words, we want to isolate the x-variable.
So, add 2y to both sides of the equation.
[tex](x-2y)+2y=(3)+2y[/tex]
On the left, the 2y cancel. Simplify the right:
[tex]x=2y+3[/tex]
And we're done!
Answer:
x = 3 + 2y
Step-by-step explanation:
This is the answer because:
1) First, you have to isolate x, in order to isolate x you have to bring x to the end of the equation.
2) Then, you have to add 2y to both sides of the equation.
Another way you can think of this is:
1) If you add 3 + 2y you would figure out the answer because if you want to find x for a subtraction equation, you can add the answer to the equation with the number.
For example, x - 20 = 10, now to figure this equation out, you can either isolate the x, or you can add the answer in the equation with the remaining number in the equation.
Hope this helps!
Find the ratio of 3 Km 300 m
Answers
Answer:
3km : 300m
3000 : 300
10 : 1
if it takes jessica 28.9 seconds to walk to the bus stop and there are 260 days she takes the bus to school a year. Then how many minutes a year does she spend walking to the buss stop? Round to the nearest minute
Answers
Answer:
Step-by-step explanation:
If there are 260 days and she takes 28.9 seconds to get to the bus stop, then that means 260 * 28.9 = 7514 seconds to get to the Stop. 7514 / 60 = number of minutes which is 125 rounded
. If T is the midpoint of SU, what are ST, TU, and SU?
Answers
Step-by-step explanation:
We have ST=5x, TU=3x+32 and they're equal if T is the midpoint:
5x = 3x + 32
2x = 32 x = 16
ST = 5x = 80
So TU = 80
and SU=160
Answer: Second choice
Need Help!! because im confused
Answers
Answer:
3g+20
Step-by-step explanation:
Because Milena wants to have 3 cups per each guest and then she wants an additional 20 more.
Answer:
C. 3g+20
Step-by-step explanation:
The answer here is 3g+20.
Their will be an additional 20 cups of punch, which is addition.
Louisa has 4 yards of fabric. She uses 2/5 yard of fabric to make a doll dress. How many doll dresses can Louisa make with the fabric? Choose the number line model that shows the answer. A. Number line from 0 to 4 is divided into 20 equal parts. Number line is grouped into 4 equal parts. B. Number line from 0 to 4 is divided into 20 equal parts. Number line is grouped into 8 parts. C. Number line from 0 to 4 is divided into 20 equal parts. Number line is grouped into 5 equal parts. D. Number line from 0 to 4 is divided into 20 equal parts. Number line is grouped into 10 equal parts.
Answers
Answer:
I believe the answer is D. Number line from 0 to 4 is divided into 20 equal parts. Number line is grouped into 10 equal parts.
Step-by-step explanation:
She can make 10 dresses if you split the number line into 20 parts and find 2/5. Therefore, it would then be grouped into 10 parts, each part 2/5ths of a yard.
Solve for f please I need help
Answers
Answer:
See Below
Step-by-step explanation:
Isolate f
h = 4 + f
-4 -4
h - 4 = f
Or f = h-4
Write 6.45 as a mixed number in simplest form.
Answers
Answer:
6 9/20
Step-by-step explanation:
6.45=645/100 = 129/120
= 6 9/20
SIMPLE QUESTION, 25 PTS: The cities G, H, and I, in respective order, lie approximately in a straight line. The distance from city G to city H is 72 miles. The distance from city G to city I is 92 miles. Find the distance from city H to city I.
Answers
Hey there! I'm happy to help!
From G to I is the total distance of the line (92). G to H is the first portion of the line (72) while H to I is the other portion.
To find H to I, simply subtract 72 from 92!
92-72=20
The distance from city H to city I is 20 miles.
Have a wonderful day! :D
Answer:
20
Step-by-step explanation:
Question 5 of 10
Solve 2x + 4 > 16.
O A. x<10
O B. x> 10
O C. x>6
O D. x< 6
Answers
Answer:
C
Step-by-step explanation:
2x +4 > 16
If you plug in 6 where the x is, and multiply 2 by 6, you get 12. Add 4 to 12 to get 16. If x is 6 it equals 16, so if x > 6 the answer will be more than 16.
can you help please??
Answers
Step-by-step explanation:
this relation is not a function cuz each x pair (domian) has only one image in y pair (codomain) so we will have all the ×-axis pairs meeting with y-axis in only one point as they have one image as this is the rule of having a function so what in front of us the positive part of x-axis has two images in y-axis
u can knew it by another way draw a vertical line and if it meets in two point or more than one then the relation is not a function s o if we draw a vertical line in the right part of the graph it will meats in two points then not a function
the domain is all the pairs of this relation taken in x-axis which are [0,infinity[ and range is the y-axis images if the fomain in x-axis which are ]-infinity, infinity[
Please Help, Im having trouble with this
Answers
Answer:
1 7/8 can be written as 8*1+7/8=15/8=1.875
Step-by-step explanation:
evaluate. (-5)^2 - (-2)^4
Answers
Answer:
9
Step-by-step explanation:
(-5)^2=25
(-2)^4=16
so therefore...25-16=9
The afternoon temperature in Biscoff Bay was – 2°F. By midnight, a warm front moved in and the temperature rose to 11°F. What was the change in temperature from afternoon to midnight? To solve the problem, Ross subtracted 11–( – 2) and came up with an answer of 13°F. Is Ross correct? Why or why not?
Answers
Answer:
Ross is correct. He is right because if you do 11- (-2) the double negatives turn into a positive and the answer is 13.
The answer is "Yes", Ross is right, and the temperature change will be 13 °F.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the mentioned data in the question,
The afternoon temperature in Biscoff Bay = -2 °F
The temperature rose at midnight = 11 °F
Then, the change in temperature will be,
It is changing from -2 °F to 11 °F then,
= 11 - (-2) = 13 °F
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A cube has a volume of 216 cubic inches. What is the length of each edge of the cube?
Answers
Volume of a cube = (edge)^3
In this problem,
Volume = 216in^2
Edge = ?
Let's plug our values into the formula above.
216in^3 = (edge)^3
Take the cbrt of both sides.
6in = edge
The length of each edge = 6in
Answer:
[tex]\boxed {\tt 6 \ centimeters}[/tex]
Step-by-step explanation:
The volume of a cube can be found using the following formula:
[tex]v=s^3[/tex]
where [tex]s[/tex] is the side length, or edge.
We know the volume is 216 cubic inches. We can substitute 216 cm³ in for [tex]v[/tex], the volume.
[tex]216 \ cm^3 = s^3[/tex]
We want to find the side length. Therefore, we must isolate the variable, [tex]s[/tex].
s is being cubed. The inverse of a cube is the cube root. Take the cube root of both sides of the equation.
[tex]\sqrt[3]{216 \ cm^3} =\sqrt[3]{s^3}[/tex]
[tex]\sqrt[3]{216 \ cm^3} =s[/tex]
[tex]6 \ cm=s[/tex]
The length of each edge of the cube is 6 centimeters.
Differentiate y=(sinx)(3x^2) please help please !
Answers
Answer:
6xsinx + 3x²cosx
Step-by-step explanation:
Differentiate using the product rule
Given y = f(x)(g(x) , then
[tex]\frac{dy}{dx}[/tex] = f(x)g'(x) + g(x)f'(x)
Here f(x) = sinx ⇒ f'(x) = cosx
g(x) = 3x² ⇒ g'(x) = 6x
Thus
[tex]\frac{dy}{dx}[/tex] = 6xsinx + 3x²cosx
the product of 25 and the number of students
Answers
Answer:
25n
25*n
Step-by-step explanation:
let n represent the number of students
3(-6+8)=(3x-6)+(3x8)
Answers
Answer:
= 6
Step-by-step explanation:
= 3 (-6 + 8)
= (3 * -6) + (3 * 8)
= -18 + 24
= 6
Answer:
[tex]x = 12[/tex]
the answer is attached to the picture
hope this helps you.
Brainliest plzz