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

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Answer 1 · 2015-08-25T03:10:24

Solve sin x = cos 2x - 1

Ans: $x = kpi$

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

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