Prove the following : root 3 cosec 20 - sec 20 = 4
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= (sqrt(3) cos 20 - sin 20))/ ( sin 20 cos 20)
= 2( sqrt(3)/2 cos 20 - (1/2) sin 20/ ( sin 20 cos 20)
= 4 ( cos 30 cos 20 - sin 30 sin 20)/ ( 2 sin 20 cos 20)
= 4 (cos (30+20))/ sin 40
= 4 cos 50/cos 50
= 4
= 2( sqrt(3)/2 cos 20 - (1/2) sin 20/ ( sin 20 cos 20)
= 4 ( cos 30 cos 20 - sin 30 sin 20)/ ( 2 sin 20 cos 20)
= 4 (cos (30+20))/ sin 40
= 4 cos 50/cos 50
= 4
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