Question

Prove that:

$\cos {15}^o-\sin {15}^o=\frac{1}{\sqrt{2}}$

Answer 1

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 \left({30}^o\right)$

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

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