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The vlaue of sqrt3cot20^(@)-4cos20^(@), ...

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

A

`1`

B

`-1`

C

`0`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
A
`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`
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