SOLUTION: prove tan^2(theta)sin^2(theta)=tan^2(theta)+cos^2(theta)-1

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Question 1188496: prove tan^2(theta)sin^2(theta)=tan^2(theta)+cos^2(theta)-1
Answer by MathLover1(20850) About Me  (Show Source):
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prove
tan%5E2%28theta%29sin%5E2%28theta%29=tan%5E2%28theta%29%2Bcos%5E2%28theta%29-1
manipulate left side
tan%5E2%28theta%29sin%5E2%28theta%29...........use identity sin%5E2%28theta%29=1-cos%5E2%28theta%29
=tan%5E2%28theta%29%281-cos%5E2%28theta%29%29
=tan%5E2%28theta%29-tan%5E2%28theta%29cos%5E2%28theta%29........use identity tan%5E2%28theta%29=sin%5E2%28theta%29%2Fcos%5E2%28theta%29
=tan%5E2%28theta%29-%28sin%5E2%28theta%29%2Fcos%5E2%28theta%29%29cos%5E2%28theta%29
=tan%5E2%28theta%29-sin%5E2%28theta%29 ........use identity sin%5E2%28theta%29=1-cos%5E2%28theta%29
=tan%5E2%28theta%29-+%281-cos%5E2%28theta%29%29
=tan%5E2%28theta%29-+1%2Bcos%5E2%28theta%29
=tan%5E2%28theta%29%2Bcos%5E2%28theta%29-1