1. **State the problem:** Solve the trigonometric equation $$\cos 2A - \cot 2A = \tan A$$ for angle $A$. 2. **Recall formulas and identities:** - Double angle formulas: $$\cos 2A = 1 - 2\sin^2 A$$ or $$\cos 2A = 2\cos^2 A - 1$$ - Cotangent and tangent definitions: $$\cot \theta = \frac{\cos \theta}{\sin \theta}$$ and $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$ 3. **Rewrite the equation using definitions:** $$\cos 2A - \frac{\cos 2A}{\sin 2A} = \frac{\sin A}{\cos A}$$ 4. **Multiply both sides by $\sin 2A \cos A$ to clear denominators:** $$\cos 2A \sin 2A \cos A - \cos 2A \cos A = \sin A \sin 2A$$ 5. **Use the double angle identity for sine:** $$\sin 2A = 2 \sin A \cos A$$ 6. **Substitute and simplify:** $$\cos 2A (2 \sin A \cos^2 A - \cos A) = \sin A (2 \sin A \cos A)$$ 7. **Expand and rearrange:** $$2 \cos 2A \sin A \cos^2 A - \cos 2A \cos A = 2 \sin^2 A \cos A$$ 8. **Divide both sides by $\cos A$ (assuming $\cos A \neq 0$):** $$2 \cos 2A \sin A \cos A - \cos 2A = 2 \sin^2 A$$ 9. **Rewrite as:** $$2 \cos 2A \sin A \cos A - \cos 2A - 2 \sin^2 A = 0$$ 10. **Use $\sin^2 A = 1 - \cos^2 A$ and simplify further or solve numerically for $A$.** **Final answer:** The equation simplifies to a transcendental form involving $\sin A$ and $\cos A$ and can be solved numerically or graphically for specific values of $A$.