SOLUTION: Find all solutions 2sin^2(x)cos(x)=cos(x)

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Question 1151360: Find all solutions
2sin^2(x)cos(x)=cos(x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2sin%5E2%28x%29cos%28x%29=cos%28x%29

2sin%5E2%28x%29cos%28x%29-cos%28x%29=0

%282sin%5E2%28x%29-1%29cos%28x%29=0......factor 2sin%5E2%28x%29-1 =>%28sqrt%282%29%29%5E2sin%5E2%28x%29-1=>%28sqrt%282%29sin%28x%29%29%5E2-1=>%28sqrt%282%29sin%28x%29-1%29%28sqrt%282%29sin%28x%29%2B1%29


%28sqrt%282%29sin%28x%29-1%29%28sqrt%282%29sin%28x%29%2B1%29cos%28x%29=0

solutions:
if %28sqrt%282%29sin%28x%29%29-1=0 => x=pi%2F4%2B2pi%2An, x=3pi%2F4%2B2pi%2An
if %28sqrt%282%29sin%28x%29%29%2B1=0=>x=5pi%2F4%2B2pi%2An, x=7pi%2F4%2B2pi%2An
if cos%28x%29=0 => x=pi%2F2%2B2pi%2An, x=3pi%2F2%2B2pi%2An
Combine all the solutions.