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

1 Answer

Aug 25, 2015

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

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