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Question

# Assertion :If In=∫tannxdx, then 6(I7+I5)=tan6x Reason: If In=∫tannxdx then In=tann−1xn−In−2∀n

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 C Assertion is correct but Reason is incorrectIn=∫tann−2x(sec2x−1)dx =∫tann−2xsec2xdx−In−2Substitute tanx=t⇒sec2xdx=dt∴In=∫tn−2dt−In−2In=tn−1n−1−In−2In=tann−1xn−1−In−2 .....(1)Substitute x=7, we have6(I7+I5)=tan6x (*)∴ Assertion (A) is true.From (1), we can conclude reason is false.Also, in Reason (R) if we substitute n=7, we getI7+I5=tan6x7⇒ 7(I7+I5)=tan6x which does not match with (*)∴ Reason (R) is false.

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