Q.81 - 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: $\tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^0\right)}$

Step-by-Step Solution

Answer

The exact value of $\tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)}$is $0$

Step 1: Given information

We are given a equation of which exact value we have to find $\tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)}$

Step 2: use the fundamental equality tan θ = sin θ cos θ

We get

$$\begin{gathered} \tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)} \\ \frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)}-\frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)} \\ =0 \end{gathered}$$

Step 3: Conclusion

The exact value of $\tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^o\right)}$ is $0.$