Question

Find the value of $\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}-2$.

Answer 1

$\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}-2$
$=\frac{\cot ({90}^{\circ }-{36}^{\circ })}{\tan {36}^{\circ }}+\frac{\tan ({90}^{\circ }-{70}^{\circ })}{\cot {70}^{\circ }}-2$
$=\frac{\tan {36}^{\circ }}{\tan {36}^{\circ }}+\frac{\cot {70}^{\circ }}{\cot {70}^{\circ }}-2$ [$\because \cot (90-\theta )=\tan \theta and\tan (90-\theta )=\cot \theta$]
$=1+1-2=0$

Hence, the answer is $0$.