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`

Explanation

`cos^2 10^@ - cos10^@cos50^@ +cos^2 50^@`

`=1/2(2cos^2 10^@ - 2cos10^@cos50^@ +2cos^2 50^@)`

`=1/2(1+cos20^@ - (cos60^@+cos40^@)+1+cos100^@)`

`=1/2(2+cos20^@ - 1/2 - cos40^@ +cos(180^@-80^@) )`

`=1/2(3/2+cos20^@ -(cos80^@+cos40^@))`

`=1/2(3/2+cos20^@ - (2cos60^@cos20^@))`

`=1/2(3/2+cos20^@ - (2(1/2)cos20^@))`

`=1/2(3/2+cos20^@ - cos 20^@)`

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