Question

How do you use the double angle formula to verify `sin4x=8cos^3xsinx-4cosxsinx`?

Answer 1

Please see below.

Explanation:

Double angle formula sates that

`sin2x=2sinxcosx` and `cos2x=2cos^2x-1`

Hence `sin4x=sin(2xx2x)=2sin2xcos2x`

= `2xx(2sinxcosx)xx(2cos^2x-1)`

= `8cos^3xsinx-4cosxsinx`