The vlaue of `cos^(2)76^(@)+cos^(2)16-cos76^(@)cos16^(@),`is

Options

A. `(-1)/(4)`
B. `(1)/(2)`
C. 0
D. `(3)/(4)`

Answer

D

Explanation

`cos^(2)76^(@)+cos^(2)16^(@)-cos76^(@)cos16^(@)[because cos(2xx76^(@))=1-2cos^(2)76^(@)`
`cos(2xx16^(@))=1-2cos^(2)16^(@)`
`2cosAcosB=cos(A+B)+cos(A-B)]`
`therefore (1)/(2)[1+cos152^(@)+1+cos32^(@)-cos92^(@)-cos60^(@)]`
`=(1)/(2)[2-(1)/(2)+cos152^(@)+cos32^(@)-cos92^(@)]`
`=(1)/(2)[(3)/(2)+2cos92^(@)cos60^(@)-cos92^(@)]`
`=(1)/(2)[(3)/(2)+cos92^(@)-cos92^(@)]=(3)/(4)`