Question

Prove that:
`sqrt(3)"cosec"20^(@)-sec20^(@)=4`

Answer 1

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