Question

The value of $\sqrt{2}\left(\cos\,15^{\circ}-\sin\,15^{\circ}\right)$ is equal to

• A. $\sqrt{3}$
• B. $\sqrt{2}$
• C. 1
• D. $2$
• E. $2\sqrt{3}$

Answer 1

Answer: (C)

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