QJEEM22Maddd6: JEE Main 2022 Mathematics - Class 11 JEEM22Maddd6 Solution: The value of 2sin (12 ∘ ) − sin (72 ∘ ) is :

Question

Verified Solution • 2025–26 Session moderate

The value of 2sin (12 $^{\circ}$ ) $-$ sin (72 $^{\circ}$ ) is :

Accepted Answer

$2 \sin 12^{\circ} - \sin 72^{\circ}$

$= \sin 12^{\circ} + (- 2 \cos 42^{\circ} . \sin 30^{\circ})$

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

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

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

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

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

Step-by-Step Verified Solution