Question

Prove that √3÷sin20° - 1÷cos20° = 4

Answer 1

you want a proof from LHS to RHS, ... 

... LHS 

= ( √3 / sin 20° ) - ( 1 / cos 20° ) 

= 2 [ (√3/2) / sin 20° ] - [ (1/2) / cos 20° ] 

= 2 [ ( sin 60° / sin 20° ) - ( cos 60° / cos 20° ) ] 

= 2 sin ( 60° - 20° ) / ( sin 20° cos 20° ) 

= 2 sin ( 2 · 20° ) / ( sin 20° cos 20° ) 

= 2 ( 2 sin 20° cos 20° ) / ( sin 20° cos 20° ) 

= 4 

= RHS ..................... QED. 

Answer 2

Hope it will help you.

Thank you