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) ]