The value of `cosycos(pi/2-x)-cos(pi/2-y)cosx+sinycos(pi/2-x)+cosxsin(pi/2-y)` is zero if (A) `x=0` (B) `y=0` (C) `x=y` (D) `npi+y-pi/4(n in Z)`

Explanation

`cosy*cos(pi/2-x)-cos(pi/2-y)cosx+sinycos(pi/2-x)+cosxsin(pi/2-y)=0`

`cosy*sinx-sinycosx+sinysinx+cosxcosy=0`

`sin(x-y)+cos(x-y)=0`

`sin(x-y)=-cos(x-y)`

`sin^2(x-y)=cos^2(x-y)`

`1-cos^2(x-y)=cos^2(x-y)`

`2cos^2(x-y)=1`

`cos^2(x-y)=1/2`

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