SOLUTION: Please help me solve this equation: (cos^2 Alpha / csc^2 Alpha) + cos^4 Alpha = cos^2 Alpha Thanks

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Question 395311: Please help me solve this equation:
(cos^2 Alpha / csc^2 Alpha) + cos^4 Alpha = cos^2 Alpha

Thanks
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
understand that csc(a)=1/sin(a)
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work with the left hand of the equation to get the right hand side
cos%5E2%28a%29%2Fcsc%5E2%28a%29%2Bcos%5E4%28a%29
= cos%5E2%28a%29%2F%281%2Fsin%5E2%28a%29%29%2Bcos%5E2%28a%29 substitute csc(a)=1/sin(a)
=cos%5E2%28a%29%2Asin%5E2%28a%29%2Bcos%5E4%28a%29 invert
=cos%5E2%28a%29%2A%28sin%5E2%28a%29%2Bcos%5E2%28a%29%29 factor out a cos^2(a)
=cos%5E2%28a%29%2A1 indetity sin%5E2%28a%29%2Bcos%5E2%28a%29=1