Question

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)`

Answer 1

`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`
`cos(x-y)=pm1/sqrt2`
`x-y=2npipmpi/4`
`x=2npipmpi/4+y`.