Q.82 - 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: 

$\cot \left({20}^o\right)-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)}$

Step-by-Step Solution

Answer

The exact value of $\cot \left({20}^o\right)-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)}$ is $0$

Step 1: Given information

We are given an trigonometric equation of which exact value is to find $\cot \left({20}^o\right)-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)}$

Step 2: use the trigonometric equality cot θ = cos θ sin θ

We get,

$$\begin{gathered} \cot \left({20}^o\right)-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)} \\ \frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)}-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)} \\ =0 \end{gathered}$$

Step 3: Conclusion

The exact value of $\cot \left({20}^o\right)-\frac{\cos \left({20}^o\right)}{\sin \left({20}^o\right)}$ is $0$