Question

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:

$\tan \left({200}^o\right)\cot \left({20}^o\right)$

Short answer

The exact value of$\tan \left({200}^o\right)\cot \left({20}^o\right)is1$

Step-by-step solution

Given information

We are given a trigonometric equation$\tan \left({200}^o\right)\cot \left({20}^o\right)$

use periodicity of the trigonometric functions tanθ+π=tanθ

We get

$$\begin{gathered} \tan \left({200}^o\right)\cot \left({20}^o\right) \\ \tan \left({180}^o+{20}^0\right)\cot \left({20}^o\right) \\ \tan \left({20}^o\right)\cot \left({20}^o\right) \\ \tan \left({200}^o\right)\frac{1}{\tan \left({20}^o\right)} \\ =1 \end{gathered}$$

Conclusion

The exact value of$\tan \left({200}^o\right)\cot \left({20}^o\right)is1$