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The value of cos^(2)48^(@)-sin^(2)12^(@)...

The value of `cos^(2)48^(@)-sin^(2)12^(@)` is

A

`(sqrt(5)+1)/(8)`

B

`(sqrt(5)-1)/(8)`

C

`(sqrt(5)+1)/(5)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Given expression, `" "cos^(2)48^(@)-sin^(2)12^(@)`
`" "=cos(48^(@)+12^(@))-cos(48^(@)-12^(@))`
`" "=cos60^(@)*cos36^(@)` ltBrgt `" "=(1)/(2)*(sqrt(5)+1)/(4)`
`" "=(sqrt(5)+1)/(8)`
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