( 10 ) (3 10 )= - Vidyadip

MCQ

$\sin \left(\frac{\pi}{10}\right) \sin \left(\frac{3 \pi}{10}\right)=$

A
$\frac{1}{2}$
B
$\frac{-1}{2}$
✓
$\frac{1}{4}$
D
1

✓

Answer

Correct option: C.

$\frac{1}{4}$

(C)
$\sin \frac{\pi}{10} \sin \frac{3 \pi}{10}=\sin 18^{\circ} \cdot \sin 54^{\circ}$
$=\sin 18^{\circ} \cdot \cos 36^{\circ}$
$\ldots\left[\because \sin \left(90^{\circ}-\theta\right)=\cos \theta\right]$
$=\frac{\sqrt{5}-1}{4} \cdot \frac{\sqrt{5}+1}{4}=\frac{1}{4}$

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