Question

The value of $\frac{cot54°}{\tan 36°}+\frac{\tan 20°}{cot70°}$ is

• A. $2$
• B. $3$
• C. $1$
• D. $0$

Answer 1

The correct option is A

$2$

Explanation for the correct option:

Find the value of the given trigonometric expression

Given, $\frac{cot54°}{\tan 36°}+\frac{\tan 20°}{cot70°}$

$$\begin{gathered} \frac{cot54°}{\tan 36°}+\frac{\tan 20°}{cot70°}=\frac{cot({90}^{\circ }-{36}^{\circ })}{\tan {36}^{\circ }}+\frac{\tan ({90}^{\circ }-{20}^{\circ })}{cot{70}^{\circ }} \\ =\frac{\tan {36}^{\circ }}{\tan {36}^{\circ }}+\frac{cot{70}^{\circ }}{cot{70}^{\circ }}\left[\because cot({90}^{\circ }-{\theta }^{\circ })=\tan {\theta }^{\circ }\&\tan ({90}^{\circ }-{\theta }^{\circ })=cot{\theta }^{\circ }\right] \\ =1+1 \\ =2 \end{gathered}$$

Hence, option (A) is the correct answer.