Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1. f(x)= -4sin^2(x)

We have been given the following function:

f(x) = -4sin²(x)

By Pythagorean identity:

sin²x + cos²x = 1. Using this in the function given above:

f(x) = -4(1 - cos²x)

⇒f(x) = -4 + 4cos²x

By half angle identity:

cos²x = 1/2[1-cos(2x)]

Using this in the function above:

⇒f(x) = -4 + 4 (1/2[1-cos(2x)])

⇒f(x) = -4 + 2[1 - cos(2x)]

⇒f(x) = -4 + 2 -2cos(2x)

⇒f(x) = -2 -2cos(2x)

⇒f(x) = -2[1 + cos(2x)]

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step-by-step explanation:

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