Question

The value of $\frac{\sin 70°}{\sin 110°}$ is _____________.

Answer 1

$\begin{array}{rcl}\frac{\sin 70°}{\sin 110°}& =& \frac{\sin 70°}{\sin \left(90°+20°\right)}\\ & =& \frac{\sin 70°}{\cos 20°}\left(\mathrm{Since}\sin \left(90°+\theta \right)=\cos \theta \right)\\ & =& \frac{\sin 70°}{\cos \left(90°-70°\right)}\\ & =& \frac{\sin 70°}{\sin 70°}=1\left(\because \cos \left(90°-\theta \right)=\sin \theta \right)\end{array}$

$\mathrm{Hence}\frac{\sin 70°}{\sin 110°}=1$