Question

Find the value of $\sin {15}^0+\cos {15}^0$.

Answer 1

$\sin {15}^0+\cos {15}^0=\sin {15}^0+\cos ({90}^0-{75}^0)$
$=\sin {15}^0+\sin {75}^0$
$=\sin ({45}^0-{30}^0)+\sin ({45}^0+{30}^0)$
$=2\sin {45}^0\cos {30}^0$
$=2\times \frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{\sqrt{2}}$