Question

Solve:

$\sin {75}^o+\sin {15}^o$.

Answer 1

$\begin{array}{c}\sin {75}^0+\sin {15}^0\\ \Rightarrow \sin \left({45}^0+30\right)+\sin \left({45}^0+{30}^0\right)\\ \Rightarrow \sin {45}^0\cos {30}^0+\cos {45}^0.\sin {30}^0+\sin {45}^0.\cos {30}^0-\cos {45}^0.\sin {30}^0\\ \Rightarrow 2\sin {45}^0.\cos {30}^0=2\times \frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}=\sqrt{\frac{3}{2}}Ans.\end{array}$