Prove that tan `70^(@) = "tan " 20^(@) + 2"tan " 50^(@)`

Explanation

To prove that \( \tan 70^\circ = \tan 20^\circ + 2 \tan 50^\circ \), we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

### Step 1: Express \( \tan 70^\circ \) using the angle addition formula
Using the angle addition formula for tangent, we can express \( \tan 70^\circ \) as:
\[ \tan 70^\circ = \tan(20^\circ + 50^\circ) = \frac{\tan 20^\circ + \tan 50^\circ}{1 - \tan 20^\circ \tan 50^\circ} \]

...