Question

How do solve the equation? (Find all solutions of the equation in the interval [0, 2π). sin(2x) − sin(x) = 0

Answer 1

`x = kpi`
`x = +- pi/3 + 2kpi`

Explanation:

sin 2x - sin x = 0
2sin x.cos x - sin x = 0
sin x(2cos x - 1) = 0
Either one of the factor should be zero.
a. sin x = 0
Unit circle gives --> x = 0, `x = pi, x = 2pi`
General answer `x = kpi`
b. 2cos x - 1 = 0 --> `cos x = 1/2`
Trig table and unit circle give:
`x = +- pi/3 + 2kpi`