15^ =? - Vidyadip

MCQ

$\cos 15^{\circ}=?$

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

✓

Answer

(b) $\frac{(\sqrt{3}+1)}{2 \sqrt{2}}$
Explanation: $\cos 15^{\circ}=\cos \left(45^{\circ}-30^{\circ}\right)=\cos 45^{\circ} \cos 30^{\circ}+\sin 45^{\circ} \sin 30^{\circ}$ $=\left(\frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}\right)+\left(\frac{1}{\sqrt{2}} \times \frac{1}{2}\right)=\frac{(\sqrt{3}+1)}{2 \sqrt{2}}$

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