The value of 2 (12^ )- (72^ ) is - Vidyadip

MCQ

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
$\frac{\sqrt{3}(1-\sqrt{5})}{2}$
✓
$\frac{\sqrt{3}(1-\sqrt{5})}{4}$

✓

Answer

Correct option: D.

$\frac{\sqrt{3}(1-\sqrt{5})}{4}$

d
$\sin 12^{\circ}+\sin 12^{\circ}-\sin 72^{\circ}$

$=\sin 12^{\circ}-2 \cos 42^{\circ} \sin 30^{\circ}$

$=\sin 12^{\circ}-\sin 48^{\circ}$

$=-2 \cos 30^{\circ} \sin 18^{\circ}$

$=-2 \times \frac{\sqrt{3}}{2} \times \frac{\sqrt{5}-1}{4}$

$=\frac{\sqrt{3}}{4}(1-\sqrt{5})$

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