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Question

Solve :
( tanx+cotx)dx

A
2tan1(tanx2tanx)+C
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B
2tan1(tanx12tanx)+C
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C
tanx2tan1(cotx12tanx)+C
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D
tanx2tan1(cotx+12tanx)+C
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Solution

The correct option is B 2tan1(tanx12tanx)+C
Write tanx=sinxcosx,
and cotx=cosxsinx
Let I=(sinx+cosx)sinxcosxdx
=2(sinx+cosx)2sinxcosxdx
=2sinx+cosxsin2xdx
Put sinxcosx=t
(cosx+sinx)dx=dt
Also, sin2x=(1t2)
I=2dt1t2
=2sin1t+C
=2sin1(sinxcosx)+C
=2tan1(tanx12tanx)+C

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