if you could show me step by step please
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Start by using the very useful identity sin(2x) = 2sin(x)cos(x). We can now write
2sin(x)cos(x)sin(x) = cos(x)
2cos(x)sin^2(x) = cos(x)
2cos(x)sin^2(x) - cos(x) = 0
cos(x)*(2sin^2(x) - 1) = 0
If either factor is equal to zero, the product would be equal to zero. So now solve cos(x) = 0 and 2sin^2(x) - 1 = 0 (or sin^2(x) = 1/2) on the given interval, and then check the answers in the original equation.
2sin(x)cos(x)sin(x) = cos(x)
2cos(x)sin^2(x) = cos(x)
2cos(x)sin^2(x) - cos(x) = 0
cos(x)*(2sin^2(x) - 1) = 0
If either factor is equal to zero, the product would be equal to zero. So now solve cos(x) = 0 and 2sin^2(x) - 1 = 0 (or sin^2(x) = 1/2) on the given interval, and then check the answers in the original equation.