Question

The value of $\sin {105}^{\circ },$ is $\frac{\sqrt{3}+1}{2\sqrt{2}}$
If true then enter $1$ and if false then enter $0$

Answer 1

$\sin {105}^{\circ }=\sin ({60}^{\circ }+{45}^{\circ })$
$=\sin {60}^{\circ }\cos {45}^{\circ }+\cos {60}^{\circ }\sin {45}^{\circ }$
$=\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{2}}+\frac{1}{2}\times \frac{1}{\sqrt{2}}$
$=\frac{\sqrt{3}+1}{2\sqrt{2}}$