Question

Evaluate each of the following :
$\frac{\tan {45}^{\circ }}{\text{cosec}{30}^{\circ }}+\frac{\sec {60}^{\circ }}{\cot {45}^{\circ }}-\frac{5\sin {90}^{\circ }}{2\cos 0^{\circ }}$

Answer 1

$\frac{\tan {45}^{\circ }}{\csc {30}^{\circ }}+\frac{\sec {60}^{\circ }}{\cot {45}^{\circ }}-\frac{5\sin {90}^{\circ }}{2\cos 0^{\circ }}$

We know that,

$\csc \theta =\frac{1}{\sin \theta }$ , $\cot \theta =\frac{1}{\tan \theta }$ , $\cos \theta =\frac{1}{\sec \theta }$

$\therefore \frac{\tan {45}^{\circ }}{\csc {30}^{\circ }}+\frac{\sec {60}^{\circ }}{\cot {45}^{\circ }}-\frac{5\sin {90}^{\circ }}{2\cos 0^{\circ }}$

$=\tan {45}^{\circ }\sin {30}^{\circ }+\sec {60}^{\circ }\tan {45}^{\circ }-\frac{5\sin {90}^{\circ }\sec 0^{\circ }}{2}$

$=1\left(\frac{1}{2}\right)+\left(2\right)1-\frac{5}{2}$

$=\frac{1}{2}+2-\frac{5}{2}$

$=\frac{1}{2}-\frac{5}{2}+2$

$=\frac{1-5}{2}+2$

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

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

$=-2+2$

$=0$