Question

Given that sin(A + B) = sin A cos B + cos A sin B, find the value of sin 75${}^{\circ }$.

Answer 1

Putting A = 45${}^o$ and B = 30${}^o$ in sin (A + B) = sin A cos B + cos A sin B , we get

sin ( 45${}^o+{30}^o$) = sin45${}^o$ cos30${}^o$ + cos45${}^o$ sin 30${}^o$

$\Rightarrow sin{75}^o=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}=\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}=\frac{\sqrt{3}+1}{2\sqrt{2}}$