Question

Find the values of $\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}$

Answer 1

Given, $\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}=\frac{\tan ({90}^{\circ }-{54}^{\circ })}{\tan {36}^{\circ }}+\frac{\cot ({90}^{\circ }-{20}^{\circ })}{\cot {70}^{\circ }}$
$=\frac{\tan {36}^{\circ }}{\tan {36}^{\circ }}+\frac{\cot {70}^{\circ }}{\cot {70}^{\circ }}$

$=1+1$

$=2$