Evaluate of each of the following integral: `int_0^(pi//2)(2logcos x-logs in\ 2x)dx`

Explanation

Given,I=`int_0^(pi//2)(2logcosx-logsin2x)dx`

=`int_0^(pi//2)(logcos^2x-log2sinxcosx)dx`


=`int_0^(pi//2)(log(cos^2x/2sinxcosx))dx`

=`int_0^(pi//2)(log(cotx/2))dx...(1)`


=`int_0^(pi//2)(log(cot(pi/2+0-x)/2))dx`

=`int_0^(pi//2)(log(tanx/2))dx...(2)`

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