Question

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

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

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

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