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Question

Mathematics Question on Inverse Trigonometric Functions

Find the value of cot(tan1a+cot1a)\cot(tan^{-1}a+\cot^{-1}a)

Answer

cot(tan1a+cot1a)\cot(tan^{-1}a+\cot^{-1}a)
= cotπ2  [tan1x+cot1x=π2]\cot\frac{\pi}{2}\;[\tan^{-1}x+\cot^{-1}x=\frac{\pi}{2}]
=0