Question

How do you solve for the exact solutions in the interval [0,2pi] of `sin(3x)cosx - sinx cos(3x) = 0`?

Answer 1

`0, pi/2, and pi.`

Explanation:

Apply the trig identity: sin (a - b) = sin a.cos b - sin b.cos a.
sin (3x - x) = sin 3x.cos x - sin x.cos 3x.
sin (3x - x) = sin 2x = 0
sin 2x = 0 --> 2x = 0 --> x = 0; and
sin 2x = 0 --> `2x = pi` --> `x = pi/2`, and
sin 2x = 0 --> `2x = 2pi` --> `x = pi`