MHT CET · Maths · Trigonometric Ratios & Identities
The value of \(\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ}\) is equal to
- A \(1\)
- B \(-1\)
- C \(0\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ} = \frac{\sqrt{3} \cos 20^{\circ}}{\sin 20^{\circ}} - 4 \cos 20^{\circ} = \frac{\sqrt{3} \cos 20^{\circ} - 4 \sin 20^{\circ} \cos 20^{\circ}}{\sin 20^{\circ}}\) \(= \frac{\sqrt{3} \cos 20^{\circ} - 2 (2 \sin 20^{\circ} \cos 20^{\circ})}{\sin 20^{\circ}} = \frac{\sqrt{3} \cos 20^{\circ} - 2 \sin 40^{\circ}}{\sin 20^{\circ}}\)
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