How do you solve sin2x = sinx?

1 Answer
Aug 15, 2015

Think of the double angle formula for sin 2x

Explanation:

sin 2x = sin x
2 sin x cos x = sin x
2 sin x cos x - sin x = 0
sin x (2 cos x - 1) = 0
Solution A: sin x = 0 \Rightarrow x = kpi, k in ZZ
Solution B: 2 cos x = 1 \Rightarrow cos x = 1/2, x = pmpi/3+2kpi = pi/3(6kpm1), k in ZZ
therefore x=kpi or x = pi/3(6kpm1), k in ZZ