Question

True or False:

$\tan 2\theta +\tan 2\theta =\tan \left(4\theta \right)$

Short answer

The given statement/expression is false.

Step-by-step solution

Step 1. Given information

The given function is$\tan \left(2\theta \right)+\tan \left(2\theta \right)=\tan \left(4\theta \right)$

Step 2. True or False

From double angle formula,

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

So,

$$\begin{gathered} \tan 2\theta +\tan 2\theta \\ \frac{2\tan \theta }{1-{\tan }^2\theta }+\frac{2\tan \theta }{1-{\tan }^2\theta } \\ \frac{4\tan \theta }{1-{\tan }^2\theta }\ne \tan 4\theta \end{gathered}$$

So, it is false.