1. **Stating the problem:** Verify if the equation $$\frac{\sin x}{1 + \cos x} + \frac{\cos x}{\sin x} = \csc x$$ is true. 2. **Rewrite the left-hand side (LHS):** Combine the two fractions over a common denominator: $$\frac{\sin x}{1 + \cos x} + \frac{\cos x}{\sin x} = \frac{\sin x \cdot \sin x + \cos x (1 + \cos x)}{(1 + \cos x) \sin x}$$ 3. **Simplify the numerator:** $$\sin^2 x + \cos x + \cos^2 x$$ Recall the Pythagorean identity: $$\sin^2 x + \cos^2 x = 1$$ So the numerator becomes: $$1 + \cos x$$ 4. **Substitute back into the fraction:** $$\frac{1 + \cos x}{(1 + \cos x) \sin x}$$ 5. **Cancel common factors:** Since $$1 + \cos x \neq 0$$ (except at specific points where the expression is undefined), we can cancel: $$\frac{1 + \cos x}{(1 + \cos x) \sin x} = \frac{1}{\sin x}$$ 6. **Recognize the right-hand side (RHS):** $$\frac{1}{\sin x} = \csc x$$ 7. **Conclusion:** The original equation holds true: $$\frac{\sin x}{1 + \cos x} + \frac{\cos x}{\sin x} = \csc x$$ **Answer:** Yes, the equation is correct.