Question

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

Answer 1

$\sin \left({75}^{\circ }\right)=\sin {\left(45+30\right)}^{\circ }$

$\text{= sin30 cos45 + sin45 cos30}$

$\text{=}\frac{1}{2}\times \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}$

$\text{=}\frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}}$

$\text{=}\frac{1+\sqrt{3}}{2\sqrt{2}}$