Question

Find the value of the following:
$\csc {60}^o-\sec {45}^o+\cot {30}^o$

Answer 1

We have $cosec{60}^o=\frac{2}{\sqrt{3}},\sec {45}^o=\left(\sqrt{2}\right)$ and $\cot {30}^o=\sqrt{3}$
Consider $cosec{60}^o-\sec {45}^o+\cot {30}^o=\frac{2}{\sqrt{3}}-\sqrt{2}+\sqrt{3}=\frac{2-\sqrt{6}+3}{\sqrt{3}}=\frac{5-\sqrt{6}}{\sqrt{3}}$