Question

Prove the following:

`(cos9x - cos5x)/(sin17x - sin3x) = - (sin2x)/(cos10x)`

Answer 1

L.H.S. = `(cos9x - cos5x)/(sin17x - sin3x)`

= `(2sin((9x + 5x)/2)sin((5x - 9x)/2))/(2cos((17x + 3x)/2)sin((17x - 3x)/2)`

= `(2sin7x sin (-2x))/(2cos 10x sin7x)`

= `(-sin 2x)/(cos 10x)`

= R.H.S.