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1988

JEE Main 1988 Mathematics question on Trigonometry

The value of the expression 3cosec⁡20°−sec⁡20°\sqrt{3}\cosec 20°-\sec 20° is equal to
  1. A.
    2
  2. B.
    2sin⁡20°/sin⁡40°2\sin 20°/\sin 40°
  3. C.
    4
  4. D.
    4sin⁡20°/sin⁡40°4\sin 20°/\sin 40°
Show answer and solution

Correct option: C

Solution

√3·cosec20° - sec20° = √3/sin20° - 1/cos20°

= (√3·cos20° - sin20°) / (sin20°·cos20°)

Numerator: √3·cos20° - sin20° = 2(sin60°·cos20° - cos60°·sin20°) = 2·sin(60°-20°) = 2·sin40°

Denominator: sin20°·cos20° = sin40°/2

So the expression = 2·sin40° / (sin40°/2) = 4.

[1988]

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