Question

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:$\tan \left({40}^o\right)-\frac{\sin \left({40}^o\right)}{\cos \left({40}^0\right)}$

Short answer

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

Step-by-step solution

Given information

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

use the fundamental equality tanθ=sinθcosθ

We get

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

Conclusion

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