Question

$\frac{\sin {30}^o+\tan {45}^o-cosec{60}^o}{\sec {30}^o+\cos {60}^o+\cot {45}^o}$.

Answer 1

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

Putting the value of above trigonometric ratios, we have,

$\frac{\sin 30°+\tan 45°-\csc 60°}{\sec 30°+\cos 60°+\cot 45°}=\frac{\frac{1}{2}+1-\frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}}+\frac{1}{2}+1}$

$\Rightarrow \frac{\frac{3}{\sqrt{2}}-\frac{2}{\sqrt{3}}}{\frac{2}{\sqrt{3}}+\frac{3}{2}}$

$\Rightarrow \frac{3\sqrt{3}-4}{2\sqrt{3}}\times \frac{1}{\frac{3\sqrt{3}+4}{2\sqrt{3}}}$

$\Rightarrow \frac{3\sqrt{3}-4}{3\sqrt{3}+4}$