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Question

Write the value of tan1x + tan−11x for x > 0.

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Solution

tan-1x+tan-1y=tan-1x+y1-xy, xy<1

tan-1x+tan-11x=tan-1x+1x1-x1x,x>0=tan-1x2+10=tan-1=tan-1tanπ2=π2

tan-1x+tan-11x=π2

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