prove sin theta-2sin cube theta/2cos cube theta-cos theta=tan theta
let theta =x
so sin x - 2sin3x
2cos3x - cosx = tanx
= sinx(1 - 2sin2x)
cosx(2cos2x - 1)
=sinx[1 -2(1 -cos2x)]
cosx(2cos2x - 1)
=sinx[1 - 2 + 2cos2x]
cosx(2cos2x - 1)
=sinx[2cos2x - 1]
cosx(2cos2x - 1)
= sinx
cosx
= tanx = rhs