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Question

# Assertion :∫tan5x.tan3x.tan2xdx=ln|sec5x|5−ln|sec3x|3−ln|sec2x|2+C Reason: tan5x−tan3x−tan2x=tan5x.tan3x.tan2x

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 incorrect
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Solution

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertiontan5x=tan(2x+3x)tan5x=tan2x+tan3x1−tan2xtan3x⇒tan5x−tan2xtan3xtan5x=tan2x+tan3x⇒tan5x−tan2x−tan3x=tan2xtan3xtan5x∫tan2xtan3xtan5xdx=∫tan5xdx−∫tan2xdx−∫tan3xdx=ln|sec5x|5−ln|sec2x|2ln|sec3x|3Hence, assertion and reason both are correct. Reason is the correct explanation of assertion

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