Rewrite the given function as an equivalent function contain

Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.

Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1. f(x) = 3sin^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

f(x)= 3 sin²xcos²x

f(x)=3(sinx cos x)²

sinx cos x=(sin2x)/2

(sinx cosx)²= (sin²2x)/4

sin²2x=(1-cos4x)/2

3sin²x cos²x= 3(1-cos4x)/8