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find the value of sin 27^(@)-cos27^(@)?...

find the value of `sin 27^(@)-cos27^(@)`?

A

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

B

`-(sqrt(5-sqrt(5)))/(2)`

C

`-(sqrt(5)-1)/(2sqrt(2))`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
`sin27^(@)-sin63^(@)=-2cos45^(@)sin18^(@)`
`=-sqrt(2)((sqrt(3)-1)/(4))=-(sqrt(3)-1)/(2sqrt(2))=-(sqrt(3-sqrt(5))/(2)`
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