Question

Find the value of sin ${75}^{\circ }$

Answer 1

We have $\sin {75}^{\circ }=\sin ({45}^{\circ }+{30}^{\circ })$
$=\sin {45}^{\circ }\cos {30}^{\circ }+\cos {45}^{\circ }\sin {30}^{\circ }$
$=\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\frac{1}{2}=\frac{\sqrt{3}+1}{2\sqrt{2}}$
$\therefore \sin {75}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}$