1. **State the problem:** Prove that $$\frac{1}{\sin A} = \frac{\cos A (1 + A)}{\tan(\tan A)}$$. 2. **Analyze the given expression:** The left side is $$\frac{1}{\sin A}$$, which is the cosecant function, $$\csc A$$. 3. **Examine the right side:** $$\frac{\cos A (1 + A)}{\tan(\tan A)}$$. 4. **Recall trigonometric identities:** - $$\csc A = \frac{1}{\sin A}$$ - $$\tan x = \frac{\sin x}{\cos x}$$ 5. **Check the right side for simplification:** The term $$\tan(\tan A)$$ is unusual and not a standard identity. Since $$\tan A$$ is an angle, $$\tan(\tan A)$$ means tangent of tangent of A, which is not a standard trigonometric expression. 6. **Conclusion:** The given equation is not a standard trigonometric identity and cannot be proven true for general angle $$A$$ without additional context or constraints. Therefore, the statement $$\frac{1}{\sin A} = \frac{\cos A (1 + A)}{\tan(\tan A)}$$ is not a valid trigonometric identity.