Question

What is the value of $\sin {75}^{\circ }$?

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

Answer 1

The correct option is A $\frac{\sqrt{3}+1}{2\sqrt{2}}$

$\sin {75}^{\circ }=\sin ({30}^{\circ }+{45}^{\circ })\sin {75}^{\circ }=(\sin {30}^{\circ }\cos {45}^{\circ }+\cos {30}^{\circ }\sin {45}^{\circ })\sin {75}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}$
Hence the correct option is (a).