SOLUTION: Solve: {{{sin(2x)sin(x)=cos(x)}}}

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Question 174455: Solve:

sin%282x%29sin%28x%29=cos%28x%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solve:
sin%282x%29sin%28x%29=cos%28x%29

Use the identity sin%282alpha%29=2sin%28alpha%29cos%28alpha%29
%282sin%28x%29cos%28x%29%29sin%28x%29=cos%28x%29

Get 0 on the right side:

2sin%28x%29cos%28x%29sin%28x%29-cos%28x%29=0

Factor out cos%28x%29:

cos%28x%29%282sin%28x%29-1%29=0

Use the zero-factor principle:



where n is any integer, positive, negative or zero.

The solutions between 0 and 360° are

30°, 90°, and 150° 


Edwin