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JEE Main 202621 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2026 · 21 January · Morning Shift · Mathematics · Trigonometric Ratios & Identities

The value of cosec 10^ - 3 10^ is equal to :

The value of cosec⁡10∘−3sec⁡10∘\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ} is equal to :

Options

  1. A8
  2. B6
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

cosec⁡10°−3sec⁡10°=cos⁡10°−3sin⁡10°sin⁡10°cos⁡10°\operatorname{cosec} 10° - \sqrt{3} \sec 10° = \frac{\cos 10° - \sqrt{3} \sin 10°}{\sin 10° \cos 10°}.
Numerator: cos⁡10°−3sin⁡10°=2(12cos⁡10°−32sin⁡10°)=2cos⁡70°=2sin⁡20°\cos 10° - \sqrt{3} \sin 10° = 2\left(\frac{1}{2}\cos 10° - \frac{\sqrt{3}}{2} \sin 10°\right) = 2\cos 70° = 2\sin 20°.
Denominator: sin⁡10°cos⁡10°=12sin⁡20°\sin 10° \cos 10° = \frac{1}{2}\sin 20°.
Result =2sin⁡20°12sin⁡20°=4= \frac{2\sin 20°}{\frac{1}{2}\sin 20°} = 4.
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