1.

tan-1x+cot-1x=π/2

Answer»

Take sin on both sides sin(tan−1x+cot−1x)

We know that

tan−1x+cot−1x=pi/2, where −∞<x<∞

=sin(tan−1x+pi/2−tan−1x)

=sin(pi/2)

=1

Hence proved



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