Question

Find the value of $\frac{\cos {45}^o}{\sec {30}^o+cosec{30}^o}$

Answer 1

From trigonometric table,

$\cos 45=\frac{1}{\sqrt{2}}$

$\sec 30=\frac{2}{\sqrt{3}}$

$cosec30=2$

Therefore,

$\frac{\cos 45}{\sec 30+cosec30}$

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

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

$=\frac{\sqrt{3}}{2\sqrt{2}(\sqrt{3}+1)}\times \frac{\sqrt{2}(\sqrt{3}-1)}{\sqrt{2}(\sqrt{3}-1)}$

$=\frac{\sqrt{6}(\sqrt{3}-1)}{8}$