Question

Solve $\frac{\sin {30}^o}{\sin {45}^o}+\frac{\sin {45}^o}{\sec {60}^o}-\frac{\sin {60}^o}{\cot {45}^o}-\frac{\cos {30}^o}{\sin {90}^o}$

Answer 1

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

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

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

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

$=\frac{3}{\sqrt{2}}-\sqrt{3}$