Question

expand (sin(x))^6 in the form of cos(x)

Answer 1

Write it like \[\sin(x)=\frac{ e ^{x}-e ^{-x} }{ 2i }\] and simplify.

Answer 2

I think we can use the trig identity: \( \sin^2 x + \cos^2 x = 1 \) here to get a form of cosine.
\( \sin^2 x = 1 - \cos^2 x \)

Just rewrite: \( \sin ^6 x = \left( \sin ^2 x \right)^3 \) using the exponent property, and then apply the identity. Expand the resulting binomial cubed.