Use the formula for lowering powers to rewrite the expressio

Use the formula for lowering powers to rewrite the expression given below as an equivalent expression containing terms of the first power of cosine:

6sin⁴x

Solution

6sin4x

=6(2sin2xcos2x)

= 6(2)(2sinxcosx)(2cos^2x -1)

= 24sinxcosx(2cos^2x -1)

= 48sinxcos^3x -24sinxcosx