1. **State the problem:** Prove or verify the identity $$\frac{\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \tan A.$$\n\n2. **Recall formulas:** Use the double-angle formulas: $$\sin 2A = 2 \sin A \cos A$$ and $$\cos 2A = 2 \cos^2 A - 1.$$\n\n3. **Substitute these into the expression:**\n$$\frac{\sin A + 2 \sin A \cos A}{1 + \cos A + 2 \cos^2 A - 1} = \frac{\sin A (1 + 2 \cos A)}{\cos A + 2 \cos^2 A}.$$\n\n4. **Simplify the denominator:**\n$$\cos A + 2 \cos^2 A = \cos A (1 + 2 \cos A).$$\n\n5. **Rewrite the fraction:**\n$$\frac{\sin A (1 + 2 \cos A)}{\cos A (1 + 2 \cos A)}.$$\n\n6. **Cancel common factor $1 + 2 \cos A$:**\n$$\frac{\sin A}{\cos A} = \tan A,$$ which matches the right side of the original equation.\n\n**Final answer:** The identity is true, $$\frac{\sin A + \sin 2A}{1 + \cos A + \cos 2A} = \tan A.$$