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Prove that sqrt(3) " cosec "20^(@)-sec 2...

Prove that `sqrt(3) " cosec "20^(@)-sec 20^(@)=4`

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L.H.S. `=sqrt(3)/(sin 20^(@))-1/(cos 20^(@))=(sqrt(3)cos20^(@)-(sin20^(@))/(sin20^(@).cos20^(@)))`
`=(4(sqrt(3)/2cos20^(@)-1/2sin20^(@))/(2sin20^(@)cos20^(@)))= 4(sin60.cos20^(@)-cos60^(@).sin20^(@))/(sin 40^(@))`
`=4.(sin(60^(@)-20^(@)))/(sin40^(@)) = 4.(sin 40^(@))/(sin 40^(@)) = 4` =RHS
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