Question

Find the value of $\frac{\sin {30}^{\circ }+\tan {45}^{\circ }-\csc {60}^{\circ }}{\cot {45}^{\circ }+\cos {60}^{\circ }-\sec {30}^{\circ }}$.

Answer 1

given, $\frac{\sin {30}^{\circ }+\tan {45}^{\circ }-\csc {60}^{\circ }}{\cot {45}^{\circ }+\cos {60}^{\circ }-\sec {30}^{\circ }}$

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

$=\frac{\frac{\sqrt{3}+2\sqrt{3}-4}{2\sqrt{3}}}{\frac{2\sqrt{3}+\sqrt{3}-4}{2\sqrt{3}}}$

$=\frac{2\sqrt{3}-4}{3\sqrt{3}-4}=1$