Question

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

Answer 1

Correct Answer - D
The given expression is
`cos y sin x- sin y cos x+ sin y sin x+ cos x cos y`
`:. sin(x-y)+cos (x-y)=0`
`rArr sqrt(2) (1/sqrt(2) sin (x-y)+1/sqrt(2) cos (x-y))=0`
or `sin (x-y+pi/4)=0`
`rArr pi/4+x-y=n pi, n in Z`
`rArr x-y=n pi -pi/4, n in Z`
`rArr x=n pi-pi/4 + y`, where `n in Z`