Question

The value of $\sin {75}^{\circ }+\cos {75}^{\circ }$ is

• A. $\frac{\sqrt{3}}{\sqrt{2}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}-1}{\sqrt{2}}$
• D. $\frac{\sqrt{3}+1}{\sqrt{2}}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{\sqrt{2}}$

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