Can you answer this question please?

(1+cos2x)/(1-cos2x) = cot^2x

sesenic [268]

We will turn the left side into the right side.

$\dfrac{1 + \cos 2x}{1 - \cos2x} = \cot^2 x$

Use the identity:

$\cos 2x = \cos^2 x - \sin^2 x$

$\dfrac{1 + \cos^2 x - \sin^2 x}{1 - ( \cos^2 x - \sin^2 x)} = \cot^2 x$

$\dfrac{1 - \sin^2 x + \cos^2 x }{1 - \cos^2 x + \sin^2 x} = \cot^2 x$

Now use the identity

$\sin^2 x + \cos^2 x = 1$ solved for sin^2 x and for cos^2 x.

$\dfrac{\cos^2 x + \cos^2 x }{\sin^2 x + \sin^2 x} = \cot^2 x$

$\dfrac{2\cos^2 x}{2\sin^2 x} = \cot^2 x$

$\dfrac{\cos^2 x}{\sin^2 x} = \cot^2 x$

$\cot^2 x = \cot^2 x$

8 0

3 years ago

Why do whole numbers raised to an exponent get bigger while fractions raised to an exponent get smaller

Brilliant_brown [7]

Answer:

when you multiply a whole number by itself it will obviously get bigger.

4 to the 2nd power equals 16 because 4x4 = 16

if you were to multiply a smaller number though, it wouldn't get as big.

Each number you put to the same exponent will not get bigger at the same rate since each number isnt being multiplied by the same thing.

ex. 4 and 6 are raised to the second power both dont get multiplied by the same number 4 is multiplied by 4, and 6 by 6, therefore the bigger the number the bigger it grows.

Fractions get smaller for this reason when you have the fraction 2/3 raised to the second, both numbers must be raised. 2 to the second equals 4 while 3 to the second is 9.

1/2 to the second would then equal 1/4 since 1 to the second equals 1 and 2 to the second equals 4.

Step-by-step explanation:

5 0

3 years ago

A 70ft ladder is mounted 10ft above the ground on a fire truck. The bottom of the ladder is 40ft from the wall of a building.the

Luda [366]

Please refer to my attachments for visual guidelines.
We are going to solve your problem by using the pythagorean theorem, a^2+b^2 = c^2, where a and b are the legs of the triangle, and c is the hypotenuse (the longest side).

The length of the ladder is equal to 70ft (hypotenuse); one leg is the distance between the wall and the bottom of the ladder - 40 ft, the other leg is unknown for it is the distance between 10 ft above the ground and the top of the ladder-represented by "x". Using pythagorean theorem, a^2+b^=c^2, we have x^2+40^2 = 70^2. Solving the exponents, we have x^2 + 1600 = 4900.

Isolating the variable x, we have x^2 = 4900-1600. Futher simplying, x^2 = 3300. Thus, x = √3300 or 57.4456264654 ft.

Adding 10 ft to x, therefore, the top of the leadder is 67.4456264654 ft off the ground.

8 0

3 years ago

There is a bag filled with 5 blue, 6 red and 2 green marbles.

Kipish [7]

Answer:

the probability of getting 2 greens is 2/13

Step-by-step explanation:

6 0

2 years ago

In right triangle XYZ, ∠Y is the right angle and m∠X = 60°. If YZ = 4, what is XY?

daser333 [38]

Answer:

B is the best answer

The question is illustrated with the attached figure.

Required

Determine XY

To solve for XY, we make use of the tan function, which states that:

tan\theta = \frac{Opposite}{Hypotenuse}tanθ=

Hypotenuse

Opposite

In this case:

tan\ 60= \frac{YZ}{XY}tan 60=

XY

YZ

Substitute 4 for YZ

tan\ 60= \frac{4}{XY}tan 60=

XY

4

Make XY the subject

XY= \frac{4}{tan\ 60}XY=

tan 60

4

tan\ 60 =\sqrt 3tan 60=

3

So, the expression becomes:

XY = \frac{4}{\sqrt 3}XY=

3

4

Rationalize:

XY = \frac{4 * \sqrt 3}{\sqrt 3 * \sqrt 3}XY=

3

∗

3

4∗

3

XY = \frac{4\sqrt 3}{3}XY=

3

4

3

6 0

2 years ago