2014/062) Find the value of : sqrt(3)*( 1/sin20 ) - ( 1/cos20 )?

= (sqrt(3) cos 20 - sin 20)/ ( cos 20 sin 20)
= 4(( sqrt(3)/2 cos 20 - 1/2 sin 20)/( 2 cos 20 sin 20) (mutliply denominator and numerator by 2)
= 4( sin 60 cos 20 - cos 60 sin 20)/( sin 40) ( knowing sin 60 = sqrt(3)/2 and cos 60 = 1/2)
= 4 sin (60-20)/ sin 40 ( sin (A-B) formula)
= 4 sin 40/ sin 40
= 4