Q.84 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The exact value of $\tan \left({200}^o\right)\cot \left({20}^o\right) is 1$

Step 1: Given information

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

Step 2: use periodicity of the trigonometric functions tan θ + π = tan θ

We get

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

Step 3: Conclusion

The exact value of $\tan \left({200}^o\right)\cot \left({20}^o\right) is 1$