Please help Rewrite the given function as an equivalent func

Please help

Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1. f(x) = - 5 sin^2 (x) cos^2 (x) f(x) = (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression. Do not factor)

Solution

Solution:

f(x) = -5 sin²(x) cos²(x)

use identity;

sin²(x) (1/2) (1 - cos(2x)) and cos²(x) (1/2) (1 + cos(2x))

f(x) = -5 {(1/2) (1 - cos(2x))} {(1/2) (1 + cos(2x))}

     = -5/4 (1 - cos²(2x))

     = -5/4 sin²(2x)

Again use identity;

sin²(x) (1/2) (1 - cos(2x)) => sin²(2x) = (1/2) (1 - cos(4x))

f(x) = -5/4 sin²(2x)

     = -(5/4) (1/2) (1 - cos(4x))

     = -5/8 (1 - cos(4x))