1. Muammo: Agar $\tan \alpha = \frac{1}{2}$, $\tan \beta = \frac{1}{3}$ va $\pi < \alpha + \beta < 2\pi$ bo'lsa, $\alpha + \beta$ ning qiymatini toping. 2. Formulalar: Tangent yig'indisi formulasini ishlatamiz: $$\tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$$ 3. Qiymatlarni qo'yamiz: $$\tan(\alpha + \beta) = \frac{\frac{1}{2} + \frac{1}{3}}{1 - \frac{1}{2} \times \frac{1}{3}} = \frac{\frac{3}{6} + \frac{2}{6}}{1 - \frac{1}{6}} = \frac{\frac{5}{6}}{\frac{5}{6}}$$ 4. Soddalashtiramiz: $$\tan(\alpha + \beta) = \frac{\frac{5}{6}}{\frac{5}{6}} = \cancel{\frac{5}{6}} \div \cancel{\frac{5}{6}} = 1$$ 5. Endi $\tan(\alpha + \beta) = 1$ va $\pi < \alpha + \beta < 2\pi$ shartini hisobga olamiz. Tangent 1 ga teng bo'ladigan burchaklar $\frac{\pi}{4} + k\pi$ ko'rinishida bo'ladi. 6. $\pi < \alpha + \beta < 2\pi$ oraliqda $\alpha + \beta = \pi + \frac{\pi}{4} = \frac{5\pi}{4}$ bo'ladi. 7. Javob: $\boxed{\frac{5\pi}{4}}$ ya'ni C variant.