Question

What is the value of $\frac{\sin {45}^{\circ }\sin {30}^{\circ }}{\cos {45}^{\circ }\cos {30}^{\circ }}$?

Answer 1

We need to find the value of $\frac{\sin {45}^{\circ }\sin {30}^{\circ }}{\cos {45}^{\circ }\cos {30}^{\circ }}$.

$\sin {45}^{\circ }=\frac{1}{\sqrt{2}}$
$\sin {30}^{\circ }=\frac{1}{2}$
$\cos {45}^{\circ }=\frac{1}{\sqrt{2}}$
$\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$

$\begin{array}{cc}\frac{\sin {45}^{\circ }\sin {30}^{\circ }}{\cos {45}^{\circ }\cos {30}^{\circ }}& =\frac{\frac{1}{\sqrt{2}}\cdot \frac{1}{2}}{\frac{\sqrt{3}}{2}\cdot \frac{1}{\sqrt{2}}}\\ & =\frac{\frac{1}{2\sqrt{2}}}{\frac{\sqrt{3}}{2\sqrt{2}}}\\ & =\frac{1}{\sqrt{3}}\end{array}$