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sin 67(1)/(2)^(@)+cos67(1)/(2)^(@) is eq...

`sin 67(1)/(2)^(@)+cos67(1)/(2)^(@)` is equal to

A

`(1)/(2)sqrt(4+2sqrt(2))`

B

`(1)/(2)sqrt(4-2sqrt(2))`

C

`(1)/(4)(sqrt(4+2sqrt(2)))`

D

`(1)/(4)(sqrt(4-2sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin67(1)/(2)^(@)+cos67(1)/(2)^(@)=sqrt(1+sin135^(@))=sqrt(1+(1)/sqrt(2))` (using `cos A+sinA=sqrt(1+sin2A)`)
`=(1)/(2)sqrt(4+2sqrt(2))`
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