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Question: Answered & Verified by Expert
(1-cosx)2/7(1+cosx)9/7dx=
MathematicsIndefinite IntegrationTS EAMCETTS EAMCET 2021 (04 Aug Shift 1)
Options:
  • A 711tanx2117+C
  • B 711tanx2711+C
  • C 711cotx2117+C
  • D 117cotx2711+C
Solution:
1449 Upvotes Verified Answer
The correct answer is: 711tanx2117+C

Let, I=(1-cosx)2/7(1+cosx)9/7dx

We know, 1-cos2A=2sin2A, 1+cos2A=2cos2A

I=(2sin2x2)2/7(2cos2x2)9/7dx

=12(tan2x2)2/7cos2x2dx

=12sec2x2tanx247dx

Let, tanx2 =t

Differentiating both sides,

12sec2x2dx = dt

I=t47dt

=711t117 +C

By substituting the value, we get

I=711tanx2117 +C

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