Question

What is the value of
√3 cosec20-sec20=?​

Answer 1

√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

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