Question

Use an identity to write the expression as a single trigonometric function or as a single number.

Answer 1

We can use the following trigonometric identity to solve the exercise:

`(2\tan\theta)/(1-\tan^2\theta)=\tan 2\theta`

In this case, θ = 15°. Then, we have:

`\begin{gathered} (2\tan15\degree)/(1-\tan^215\degree)=\tan 2(15\degree) \\ (2\tan15\degree)/(1-\tan^215\degree)=\tan 30\degree \end{gathered}`

We can use a notable angles table to find the value of tan 30°. Finally, we have:

`(2\tan15\degree)/(1-\tan^215\degree)=\frac{\sqrt[]{3}}{3}`