Trig Identity

Question

Prove sin4x = 4 (sin x-2 sin^3 x)/secx

 

I can't seem to solve this! Halp!!!

Answer 1

sin(4x) = sin[2(2x)]

 

           = 2sin(2x)cos(2x)

 

           = 2[2sinxcosx](1-2sin²x)

 

           = 4sinxcosx - 8sin³xcosx

 

           = 4cosx(sinx - 2sin³x)

 

           = 4(1/secx)(sinx - 2sin³x) = 4(sinx - 2sin³x)/secx