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If sin 2theta+sin 2phi=1//2 and cos2thet...

If `sin 2theta+sin 2phi=1//2` and `cos2theta+cos 2phi=3//2`, then `cos^(2)(theta-phi)=`

A

`3//8`

B

`5//8`

C

`3//4`

D

`5//4`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `sin 2theta + sin 2phi = 1//2` …(1)
and `cos 2theta + cos 2phi = 3//2` …(2)
Square and adding,
`therefore (sin^(2)2theta + cos^(2) 2theta)+(sin^(2)2phi + cos^(2)2phi)+2[sin 2theta sin 2phi + cos 2theta cos 2phi]=1//4 + 9//4`
`rArr cos 2theta cos 2phi + sin 2theta sin 2phi = 1//4`
`rArr cos (2theta - 2phi)=1//4 rArr cos^(2) (theta - phi) = 5//8`
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