Question

#37. What is the next step when solving the equation sin (2x) - sin (x) = 0​

Answer 1

sin(2x) - sin(x) = 0

Expand the first term using the double angle identity:

2 sin(x) cos(x) - sin(x) = 0

Factor out sin(x) :

sin(x) (2 cos(x) - 1) = 0

This leaves you with 2 cases that can be solved separately:

sin(x) = 0   or   2 cos(x) - 1 = 0

sin(x) = 0   or   cos(x) = 1/2

[x = 2nπ   or   x = π + 2nπ]   or   [x = π/6 + 2nπ   or   x = 5π/6 + 2nπ]

(where n is any integer)