Question

Find the value of $\sin {15}^o-\cos {15}^o$.

Answer 1

Now,

$\sin {15}^o-\cos {15}^o$

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

$=\sqrt{2}(\cos {45}^o.\sin {15}^o-\sin {45}^o.\cos {15}^o)$

$=-\sqrt{2}\sin ({45}^o-{15}^o)$

$=-\sqrt{2}\sin {30}^o$

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

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