SOLUTION: Find the zeros: f(x)= sin2xsinx-cosx Thanks

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Question 957663: Find the zeros:
f(x)= sin2xsinx-cosx

Thanks
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the zeros: For [0,2π)
f(x)= sin2xsinx-cosx =2sinxcosxsinx-cosx=cosx(2sin^2x-1)=0
cosx=0
x=π/2, 3π/2
or
2sin^2(x)-1=0
sin^2(x)=1/2
sinx=±√(1/2)=±√2/2
x=π/4,3π/4,5π/4,7π/4