Question

Without using calculator find the value of $\sin \left({105}^o\right)$.

Answer 1

$\sin \left({105}^o\right)$

$=\sin ({60}^o+{45}^o)$

$(\therefore \sin (a+b)=\sin a\cos b+\cos a\sin b)$

$\Rightarrow \sin {60}^o\cos {45}^o+\cos {60}^o\sin {45}^o$

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

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

or $\frac{\sqrt{6}+\sqrt{2}}{4}=\sin \left({105}^o\right)$