12 =? - Vidyadip

MCQ

$\sin \frac{\pi}{12}=?$

A
$\frac{(\sqrt{3}+1)}{2 \sqrt{2}}$
B
$\frac{(\sqrt{3}-1)}{2 \sqrt{2}}$
C
$\frac{(2 \sqrt{3}+1)}{2 \sqrt{5}}$
D
$\frac{-(\sqrt{3}-1)}{2}$

✓

Answer

(b) $\frac{(\sqrt{3}-1)}{2 \sqrt{2}}$
Explanation: $\sin \frac{\pi}{12}=\sin \left(\frac{\pi}{4}-\frac{\pi}{6}\right)=\sin \frac{\pi}{4} \cos \frac{\pi}{6}-\cos \frac{\pi}{4} \sin \frac{\pi}{6}$
$=\left(\frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}\right)-\left(\frac{1}{\sqrt{2}} \times \frac{1}{2}\right)=\frac{(\sqrt{3}-1)}{2 \sqrt{2}}$

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