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NDA 2021 Maths · Mathematics · Trigonometric Functions and Identities · hard

The value of (1)/(sin 10^°)-(√3)/(cos 10^°) is

Single correct option

The value of 1sin⁡10∘−3cos⁡10∘\dfrac1{\sin10^\circ}-\dfrac{\sqrt3}{\cos10^\circ} is
  1. A. 22
  2. B. 88
  3. C. 11
  4. D. 44
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Answer: (D) 44

Combine: cos⁡10∘−3sin⁡10∘sin⁡10∘cos⁡10∘=2cos⁡70∘12sin⁡20∘=2sin⁡20∘12sin⁡20∘=4\frac{\cos10^\circ-\sqrt3\sin10^\circ}{\sin10^\circ\cos10^\circ}=\frac{2\cos70^\circ}{\frac12\sin20^\circ}=\frac{2\sin20^\circ}{\frac12\sin20^\circ}=4, using cos⁡70∘=sin⁡20∘\cos70^\circ=\sin20^\circ.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake