The value of `sqrt3cot20^(@)-4cos20^(@)` is

Options

A. `1`
B. `-1`
C. `0`
D. non of these

Answer

A

Explanation

`sqrt(3)cot 20^(@)-4cos 20^(@)`
`=(sqrt(3)cos20^(@))/(sin20^(@))-4cos 20^(@)`
`=(sqrt(3)cos 20^(@)-4sin20^(@)cos20^(@))/(sin20^(@))`
`=(2[sqrt(3)/(2)cos 20^(@)-2sin20^(@)cos20^(@)])/(sin20^(@))`
`=(2(sin60^(@)cos20^(@)-sin40^(@)))/(sin20^(@))`
`=([2sin60^(@)cos20^(@)-2sin40^(@)])/(sin20^(@))`
` =(sin80^(@)+sin40^(@)-2sin40^(@))/(sin20^(@))`
`=(sin80^(@)-sin40^(@))/(sin20^(@))`
`=(2cos60^(@).sin20^(@))/(sin20^(@))`
`2xos60^(@)=1`