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Question

Prove the identity :
(tanθ+cotθ)2(tanθcotθ)2=4

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Solution

(tanθ+cotθ)2(tanθcotθ)2=4
L.H.S=(tanθ+cotθ)2(tanθcotθ)2
=(tanθ+cotθ+tanθcotθ)(tanθ+cotθtanθ+cotθ)
=2tanθ×2cotθ
=4
L.H.S=R.H.S
Hence, the answer is proved.

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