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Question

Prove that:
tan1a+cot1(a+1)=tan1(a2+a+1).

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Solution

Since cotx=1tanx,
cot1x=tan11x
So, we have,
tan1a+cot1(a+1)=tan1a+tan11a+1
=tan1(a+1a+11aa+1)=tan1(a2+a+1)

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