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Question

I=a0ln(cot a+tan x)dx, where aϵ(0,π2), then I is equal to


A

aln(sina)

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B

aln(sina)

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C

2aln(cosa)

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D

2aln(sina)

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Solution

The correct option is A

aln(sina)


I=a0ln(cot a+tan x)dx

=a0ln(cos(ax)sin a cos x)dx ...(1)

I=a0ln(cos xsin a cos (ax))dx ...(2)

Adding (1) and (2) we get 2I=a0ln(1sin2a)dx

2I=2a0ln(sin a)dx

I=a ln (sin a)


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