The value of following is `cos24^(@)+cos55^(@)+cos125^(@)+cos204^(@)+cos300^(@)`

Options

A. `-1//2`
B. `1//2`
C. `2`
D. `1`

Answer

b

Explanation

The value of `cos24^(@)+cos55^(@)+cos125^(@)+cos204^(@)+cos300^(@)`
We know that `cos(180^(@)+-theta)`
`=-cos theta`
`rArr cos24^(@)+cos55^(@)+cos(180^(@)-55^(@))+cos(180^(@)+24^(@))=cos(360^(@)-60^(@))`
`rArrcos24^(@)+cos55^(@)-cos55^(@)-cos24^(@)+cos60^(@)`
`rArrcos 60^(@)=(1)/(2)`