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Evaluate: int0^(pi//2)(s in x-cosx)/(1+s...

Evaluate: `int_0^(pi//2)(s in x-cosx)/(1+s in xcosx)dx`

Text Solution

Verified by Experts

Let,I=`int_0^(pi//2)(sin x-cosx)/(1+sinx.cosx)dx...(1)`
using `int_a^b​f(x)dx=int_a^b​f(a+b−x)dx`
I=`int_0^(pi//2)(cos x-sinx)/(1+sinx.cosx)dx...(1)`
(1)+(2)
`2I=int_0^(pi//2) 0dx`
`I=0`
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