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MHT CET · Maths · Trigonometric Ratios & Identities

The value of \(\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ}\) is equal to

  1. A \(1\)
  2. B \(-1\)
  3. C \(0\)
  4. D \(\frac{1}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(1\)

Step-by-step Solution

Detailed explanation

\(\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ} = \frac{\sqrt{3} \cos 20^{\circ}}{\sin 20^{\circ}} - 4 \cos 20^{\circ} = \frac{\sqrt{3} \cos 20^{\circ} - 4 \sin 20^{\circ} \cos 20^{\circ}}{\sin 20^{\circ}}\) \(= \frac{\sqrt{3} \cos 20^{\circ} - 2 (2 \sin 20^{\circ} \cos 20^{\circ})}{\sin 20^{\circ}} = \frac{\sqrt{3} \cos 20^{\circ} - 2 \sin 40^{\circ}}{\sin 20^{\circ}}\)