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(cos^2 3 3^(@)-cos^2 5 7^@)/(sin2 1^@-co...

`(cos^2 3 3^(@)-cos^2 5 7^@)/(sin2 1^@-cos2 1^@)=`

A

`(1)/(sqrt(2))`

B

`-(1)/(sqrt(2))`

C

`(sqrt(3))/(2)`

D

`-(sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(cos^(2)33^(@)-cos^(2)57^(@))/(cos 69^(@)-cos 21^(@))`
`=(sin(57^(@)+33^(@))sin(57^(@)-33^(@)))/(-2sin.(69^(@)+212^(@))/(2)sin.(69^(@)-21^(@))/(2))`
`=(sin90^(@)xx sin 24^(@))/(-2sin 45^(@)sin 24^(@))`
`=(1)/(-2xx(1)/(sqrt(2)))=-(1)/(sqrt(2))`
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