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The value of cosycos(pi/2-x)-cos(pi/2-y)...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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`
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