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)

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