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The value of cos^2 10^0-cos10^0cos50^0+c...

The value of `cos^2 10^0-cos10^0cos50^0+cos^2 50^0` is equal to `4/3` (b) `1/3` (c) `3/4` (d) `3`

A

`(4)/(3)`

B

`(1)/(3)`

C

`(3)/(4)`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2)10^(@)-cos10^(@)cos50^(@)+cos^(2)50^(@)`
`=(1)/(2)[1+cos 20^(@)-(cos60^(@)+cos40^(@))`
`+(1+cos 100^(@))]`
`=(1)/(2)[1+cos20^(@)-(1)/(2)-cos40^(@)+1-cos80^(@)]`
`=(1)/(2)[(3)/(2)+cos 20^(@)-(2cos 60^(@)cos20^(@))]=(3)/(4)`
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