If int(0)^(pi//2) log cos x dx =(pi)/(...

If `int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)),` then `int_(0)^(pi//2) log sec x dx =`

A

`(pi)/2 log(1/2)`

B

`1-(pi)/2log(1/2)`

C

`1+(pi)/2log(1/2)`

D

`(pi)/2log2`

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The correct Answer is:

D

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