Prove an Identity help!
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Prove an Identity help!

[From: ] [author: ] [Date: 11-12-06] [Hit: ]
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Prove this identity:

cos^2y - sin^2y = (1-tan^2y) / 1 + tan^2y

Please show all steps as clearly as possible as i would like to understand what exactly is going on - comments throughout the solution explaining what is going on would be greatly appreciated!!

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RHS = (1-tan²y)/(1+tan²y)

Multiply numerator and denominator by cos²y
(note that tan²ycos²y = sin²y)

RHS = (1*cos²y-tan²ycos²y)/(1*cos²y+tan²ycos²y…‡
(cos²y - sin²y)/(cos²y +sin²y)

Since cos²y + sin²y =1

RHS = (cos²y - sin²y)/1 = LHS
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