Question

$\frac{\sin 30°}{\cos 45°}+\frac{\cot 45°}{\sec 60°}-\frac{\sin 60°}{\tan 45°}-\frac{\cos 30°}{\sin 90°}$

Answer 1

On substituting the values of various T-ratios, we get:

$$\begin{gathered} \frac{\sin {30}^{\mathrm{o}}}{\cos {45}^{\mathrm{o}}}+\frac{\cot {45}^{\mathrm{o}}}{\sec {60}^{\mathrm{o}}}-\frac{\sin {60}^{\mathrm{o}}}{\tan {45}^{\mathrm{o}}}-\frac{\cos {30}^{\mathrm{o}}}{\sin {90}^{\mathrm{o}}} \\ =\frac{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.}}+\frac{1}{2}-\frac{{\displaystyle \raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{1}-\frac{{\displaystyle \raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{1} \\ =\frac{\sqrt{2}}{2}+\frac{1}{2}-\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2} \\ =\frac{\left(\sqrt{2}+1-2\sqrt{3}\right)}{2} \end{gathered}$$