Question

How do you solve `sin2x = sinx`?

Answer 1

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`