JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The value of \(2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)\) is
- A \(\frac{\sqrt{5}(1-\sqrt{3})}{4}\)
- B \(\frac{1-\sqrt{5}}{8}\)
- C \(\frac{\sqrt{3}(1-\sqrt{5})}{2}\)
- D \(\frac{\sqrt{3}(1-\sqrt{5})}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{3}(1-\sqrt{5})}{4}\)
Step-by-step Solution
Detailed explanation
\(\sin 12^{\circ}+\sin 12^{\circ}-\sin 72^{\circ}\) \(=\sin 12^{\circ}-2 \cos 42^{\circ} \sin 30^{\circ}\) \(=\sin 12^{\circ}-\sin 48^{\circ}\) \(=-2 \cos 30^{\circ} \sin 18^{\circ}\) \(=-2 \times \frac{\sqrt{3}}{2} \times \frac{\sqrt{5}-1}{4}\)…
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