Question

The value of $\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}$ is

• A. $0$
• B. $2$
• C. $3$
• D. $1$

Answer 1

Answer: (B)

$2$

$\frac{\cot {54}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\cot {70}^{\circ }}$

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

$=\frac{\tan {36}^{\circ }}{\tan {36}^{\circ }}+\frac{\tan {20}^{\circ }}{\tan {20}^{\circ }}$

$=1+1=2$