Question

Rewrite
`sin^(4)x\\` so that it involves only the first power of cosine

Show work and reasoning. Please helpp

Answer 1

sin^4 x = sin^2 x * sin^2 x

sin^4 x = (1 - cos^2 x)(1 - cos^2 x)

sin^4 x = (1 - cos x)(1 + cos x)(1 - cos x)(1 + cos x)

sin^4 x = (1 - cos x)2 * (1 + cos x)^2

Either of the last two equivalent expressions will work, as they both only involve cosine to the first power.