A solution of the equation tan−1⁡(1+x)+tan−1⁡(1−x)=π2, is

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x=1

x=-1

x=0

x=π

answer is C.

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Detailed Solution

We have, tan−1⁡(1+x)+tan−1⁡(1−x)=π2⇒ tan−1⁡(1+x)=π2−tan−1⁡(1−x) ⇒ tan−1⁡(1+x)=cot1⁡(1−x)⇒ tan−1⁡(1+x)=tan−1⁡11−x⇒ 1+x=11−x⇒1−x2=1⇒x=0

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