Question

root3
$\sqrt{3} cosec20 - sec20 = 4$
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Answer 1

Answer     : PLEASE  MARK  AS   BRAINLIEST

hope this helps you..................

Step-by-step explanation:  

√3 cosec 20° - sec 20°

= √3/ sin 20° - 1/ cos 20°

= √3cos 20° - sin 20°/ sin 20° cos 20°

= 4 [√3/2 cos 20° - 1/2 sin 20° / 2 sin 20° cos 20°]

= 4 [ sin 60° cos 20° - cos 60° sin 20°/ sin 40°] -- ( 2 sin A cos A = sin 2A)

Using identity sin ( A - B ) = sin A cos B - cos A sin B

= 4 sin (60° - 20°) / sin 40°

= 4 sin 40°/ sin 40°

= 4

Required Answer is 4