SOLUTION: Find all solutions of the equation in the interval [0, 2π) sin(x + π/4) − sin(x − 5π/4) = sqrt 2/2

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Question 872509: Find all solutions of the equation in the interval [0, 2π)
sin(x + π/4) − sin(x − 5π/4) = sqrt 2/2
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions of the equation in the interval [0, 2π)
solve for x
sin%28x+%2B+pi%2F4%29-+sin%28x+-+5pi%2F4%29+=+sqrt%282%29%2F2
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sin%28x%2Bpi%2F4%29=sinx%2Acos%28pi%2F4%29%2Bcosx%2Asin%28pi%2F4%29

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sin%28x-5pi%2F4%29=sinx%2Acos%285pi%2F4%29-cosx%2Asin%285pi%2F4%29

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sqrt%282%29sinx=sqrt%282%29%2F2
sinx=1%2F2
x=π/6, 5π/6