1.

`int_(0)^(pi//2) ""(sin x - cos x)/( 1-sin x * cos x) dx ` is equal to

Answer» Correct Answer - A
Let `I=int_(0)^(pi//2)""(sin x - cos x)/( 1- sinx cos x) dx` .......(i)
On putting ` x=((pi)/(2)-x)` in Eq. (i) , we get
`I=int_(0)^(pi//2)(sin((pi)/(2)-x)-cos((pi)/(2)-x))/(1-sin((pi)/(2)-x)cos""((pi)/(2)-x))dx `
`implies int_(0)^(pi//2)( cos x- sin x)/( 1- sinx cos s) dx`
`implies int_(0)^(pi//2)""((sin x - cos x)/( 1- sinx cosx )) dx`
On adding Eqs. (i) and (ii) ,we get
`2I=int_(0)^(pi//2) 0 dx=0`
`impliesI=0`


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