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3.Trigonometrical Ratios, Functions and Identities
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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
$\frac{\sqrt{3}(1-\sqrt{5})}{4}$
(JEE MAIN-2022)
Solution
$\sin 12^{\circ}+\sin 12^{\circ}-\sin 72^{\circ}$
$=\sin 12^{\circ}-2 \cos 42^{\circ} \sin 30^{\circ}$
$=\sin 12^{\circ}-\sin 48^{\circ}$
$=-2 \cos 30^{\circ} \sin 18^{\circ}$
$=-2 \times \frac{\sqrt{3}}{2} \times \frac{\sqrt{5}-1}{4}$
$=\frac{\sqrt{3}}{4}(1-\sqrt{5})$
Standard 11
Mathematics
