Question

How do you find the general solutions for `sinx = cos2x - 1`?

Answer 1

Solve sin x = cos 2x - 1

Ans: `x = kpi`

Explanation:

Use trig identity: `cos 2x = 1 - 2sin^2 x`
`sin x = 1 - 2sin^2 x - 1`
`3sin^2 x = 0`
`sin x = 0 -->`x = 0`and`x = pi#

General solutions:
`x = kpi`
Check> x = pi --> sin x = 0, cos 2x = cos 2pi = 1
We get 0 = 1 - 1. OK