How do you express sin4x as a trigonometric funcition of x using the identities? I think that you are supposed to start with the sine sum identity and then use the double angle identities for sin2A and cos2A, but after that I get stuck...

Answer 1

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

this is expressed in terms of trig functions of x.