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} $
$= \frac{1}{\sqrt{2}}$