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Question

Assertion :31{tan1(x1+x2)+tan1(x2+1x)}dx=2π Reason: tan1x+cot1x=π2 and tan1t=cot11t

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
31{tan1(x1+x2)+tan1(1+x2x)}dx
=31{tan1(x1+x2)+cot1(x1+x2)}dx
=π231dx as Reason (R) is correct [tan1x+cot1x=π2]
=π2(3+1)=2π
31{tan1(x1+x2)+tan1(1+x2x)}dx=2π
Hence, both assertion and reason are correct and reason is the correct explanation for assertion.

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