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Prove the following trigonometric identities: tan^2A+cot^2A=sec^2Acosec^2A - 2

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Prove the following trigonometric identities:

 tan2A+cot2A=sec2Acos2A - 2

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R.H.S = sec2Acos2A - 2

=(1+tan2A)(1+cot2A) - 2

=(tan2A+cot2A+tan2A cot2A+1) - 2

=(tan2A+cot2A+1+1) - 2

=(tan2A+cot2A)

= LHS

Hence Proved.

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