Question

How do you find all solutions of the equation `sin(3x)cosx-sinx cos(3x)=0`?

Answer 1

Trig identity: `sin (a - b) = sin a.cos b - sin b.cos a`

`f(x) = sin (3x - x) = sin 2x = 0 -> 2x = 0; and 2x = 2Pi; and 2x = Pi`

`2x = 0 -> x = 0`

`2x = 2Pi -> x = Pi`

`2x = Pi -> x = Pi/2`