What is the value of `cos10^(@)+cos110^(@)+cos130^(@)`?

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

B

Explanation

Consider cos `10^(@)+cos110^(@)+cos130^(@)`
`=cos130^(@)+cos10^(@)+cos110^(@)` `=2cos((130+10)/(2))cos((130-10)/(2))+cos110^(@)`
`=2cos((140)/(2))cos((120)/(2))+cos110^(@)`
`=2cos60^(@)cos70^(@)+cos110^(@)`
`=cos70^(@)+cos110^(@)(because"cos "60^(@)(1)/(2))`
`=cos(180^(@)-110^(@))+cos110^(@)`
`=-cos110^(@)+cos110^(@)=0(becausecos(180^(@)-theta)=-costheta)`