साबित करें कि `sqrt(3) cosec 20^(@) - sec 20^(@) = 4 `

Explanation

बायाँ पक्ष `=(sqrt(3))/(sin 20^(@))-(1)/(cos20^(@))= (sqrt(3)cos20^(@)-sin20^(@))/(sin20^(@)cos20^(@))`
`= (2(sqrt(3)/(2)cos20^(@)-(1)/(2)sin20^(@)))/(sin 20^(@)cos20^(@))`
`= (2(sin 60^(@)cos 20^(@) -cos 60^(@) sin 20^(@)))/(sin 20^(@) cos 20^(@))`
`= ( 2sin ( 60^(@) - 20^(@)))/(sin 20^(@) cos 20^(@)) = ( 2sin 40^(@))/( sin 20^(@) cos 20^(@))`
`= ( 4sin 40^(@))/( 2 sin 20^(@) cos 20^(@)) = ( 4 sin 40^(@))/( sin 40^(@)) =4 `