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If x =cos alpha+cos beta-cos(alpha+beta)...

If `x =cos alpha+cos beta-cos(alpha+beta)` and `y=4 sin.(alpha)/(2)sin.(beta)/(2)cos.((alpha+beta)/(2))`, then (x-y) equals

A

0

B

1

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=4 sin.(alpha)/(2)sin.(beta)/(2)cos((alpha+beta)/(2))`
`=2[cos.(alpha-beta)/(2)-cos.(alpha+beta)/(2)]cos((alpha+beta)/(2))`
`= cos alpha + cos beta - (1+cos (alpha + beta))=x-1`
`rArr x-y=1`
`cos 5^(@)cos 20^(@)+cos 35^(@)cos 50^(@)`
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