tgα + ctgβ = ctg a + tgβ tga = tgβ

Решение:

1. $$t g \alpha + c t g \beta = \frac{t g \alpha + \frac{1}{t g \beta}}{\frac{1}{t g \alpha} + t g \beta} = \frac{t g \alpha \cdot t g \beta + 1}{c t g \alpha \cdot t g \beta + t g^2 \beta}$$
2. $$\frac{t g \alpha}{t g \beta} = t g \alpha \cdot c t g \beta$$.

Ответ: tgα + ctgβ = $$\frac{t g \alpha \cdot t g \beta + 1}{c t g \alpha \cdot t g \beta + t g^2 \beta}$$, tga/tgβ = tgα ⋅ ctg β