SOLUTION: Prove each identity: tan^2x sin^2x = tan^2x-sin^2x

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Question 1104470: Prove each identity:
tan^2x sin^2x = tan^2x-sin^2x
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Work on the right hand side to make it the same as the left hand side...

tanx%5E2+-+sinx%5E2

= sinx%5E2%2Fcosx%5E2-sinx%5E2 [change to sinx and cosx]

= %28sinx%5E2-sinx%5E2%2Acosx%5E2%29%2Fcosx%5E2 [common denominator...]

= %28sinx%5E2%281-cosx%5E2%29%29%2Fcosx%5E2 [common factor...]

= %28sinx%5E2%2Asinx%5E2%29%2Fcosx%5E2 [basic trig identity]

= sinx%5E2%2A%28sinx%5E2%2Fcosx%5E2%29

= sinx%5E2%2Atanx%5E2