1. **State the problem:** Solve the equation $$\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{5}{\cos x}$$ for $$0 < x < \pi$$, giving answers in radians to 3 significant figures. 2. **Rewrite the equation:** Note that $$\frac{\sin x}{\cos x} = \tan x$$ and $$\frac{\cos x}{\sin x} = \cot x$$, so the left side is $$\tan x + \cot x$$. 3. **Express in terms of sine and cosine:** $$\tan x + \cot x = \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \frac{1}{\sin x \cos x}$$ 4. **Rewrite the original equation:** $$\frac{1}{\sin x \cos x} = \frac{5}{\cos x}$$ 5. **Multiply both sides by $$\sin x \cos x$$ to clear denominators:** $$1 = 5 \sin x$$ 6. **Solve for $$\sin x$$:** $$\sin x = \frac{1}{5} = 0.2$$ 7. **Find $$x$$ in the interval $$0 < x < \pi$$:** Since $$\sin x = 0.2$$, the solutions are: $$x = \arcsin(0.2)$$ and $$x = \pi - \arcsin(0.2)$$ 8. **Calculate values to 3 significant figures:** $$x_1 = 0.201$$ radians $$x_2 = 2.94$$ radians **Final answers:** $$x = 0.201$$ or $$x = 2.94$$ radians (to 3 significant figures).