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The vlaue of cos^(2)76^(@)+cos^(2)16-cos...

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

A

`(-1)/(4)`

B

`(1)/(2)`

C

0

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`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)`
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Knowledge Check

  • Statement-1: The vlaue of cos20^(@)cos40^(@)cos60^(@)cos80^(@)is1/16. Statement-2: for any theta, cos thetacos(60^(@)-theta)cos(60^(@)+theta)=1/4cos3theta

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    Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
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    Statement-1 is True, Statement-2 is False.
    D
    Statement-1 is False, Statement-2 is True.

  • The value of (3+cot76^(@)cot16^(@))/(cot76^(@)+cot16^(@)) is

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    `cot44^(@)`
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    `cot46^(@)`
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  • Solve (3+cot76^(@)cot16^(@))/(cot76^(@)+cot16^(@))=

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