Rewrite cos4x as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Someone do this pls

To rewrite cos(4x) as an equivalent expression without powers of trigonometric functions greater than 1, we can use the multiple angle formula for cosine:

cos(2θ) = 2cos²(θ) - 1.

Let's apply this formula to our expression:

cos(4x) = cos(2(2x))
= 2cos²(2x) - 1.

Now, we can further simplify by using the multiple angle formula again:

cos(2x) = 2cos²(x) - 1.

Replacing this value back into our expression, we get:

cos(4x) = 2(cos²(2x)) - 1
= 2(2cos²(x) - 1) - 1
= 4cos²(x) - 3.

Therefore, an equivalent expression for cos(4x) without powers of trigonometric functions greater than 1 is 4cos²(x) - 3.

To rewrite cos^4(x) as an equivalent expression without powers of trigonometric functions greater than 1, we can use the double angle formula and the power reduction formula.

The double angle formula states that: cos(2x) = 2cos^2(x) - 1

Using the double angle formula, we can express cos^4(x) as: [2cos^2(x) - 1]^2

Simplifying this expression, we have: [2cos^2(x) - 1]^2 = 4cos^4(x) - 4cos^2(x) + 1

Therefore, cos^4(x) can be rewritten as: 4cos^4(x) - 4cos^2(x) + 1, which does not contain powers of trigonometric functions greater than 1.

asd