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:

$\frac{2\tan\theta}{1-\tan^2\theta}=\tan 2\theta$

In this case, θ = 15°. Then, we have:

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

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

$\frac{2\tan15\degree}{1-\tan^215\degree}=\frac{\sqrt[]{3}}{3}$