Question

The value of $\cos 15^{\circ }-\sin 15^{\circ }$ is

• A. 0
• B. $\frac{1}{\sqrt{2}}$
• C. $-\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2\sqrt{2}}$

Answer 1

Answer: (B)

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