Question

With the help of result $\sin (A+B)=\sin A\cdot B+\cos A\cdot \sin B$, find the value of $\sin 75$.

Answer 1

$\sin {75}^o$

$=\sin ({45}^o+{30}^o)$

$=\sin {45}^o\cos {30}^o+\cos {45}^o\sin {30}^o\left(\sin \right(A+B)=\sin A\cos B+\cos A\sin B)$

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

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

$=\frac{\sqrt{2}(\sqrt{3}+1)}{4}$

$\therefore \sin {75}^o=\frac{\sqrt{2}}{4}(\sqrt{3}+1)$.