Trojuholník ABC

Tangensová veta alebo tangentová veta je v trigonometrii tvrdenie o rovinných trojuholníkoch.

Pre každý trojuholník ABC s vnútornými uhlami α, β, γ a stranami a, b, c platí:

${\displaystyle {\frac {a-b}{a+b}}={\frac {\mathrm {tg} \,{\frac {\alpha -\beta }{2}}}{\mathrm {tg} \,{\frac {\alpha +\beta }{2}}}}={\frac {\mathrm {tg} \,{\frac {\alpha -\beta }{2}}}{\mathrm {cotg} \,{\frac {\gamma }{2}}}}}$

${\displaystyle {\frac {b-c}{b+c}}={\frac {\mathrm {tg} \,{\frac {\beta -\gamma }{2}}}{\mathrm {tg} \,{\frac {\beta +\gamma }{2}}}}={\frac {\mathrm {tg} \,{\frac {\beta -\gamma }{2}}}{\mathrm {cotg} \,{\frac {\alpha }{2}}}}}$

${\displaystyle {\frac {c-a}{c+a}}={\frac {\mathrm {tg} \,{\frac {\gamma -\alpha }{2}}}{\mathrm {tg} \,{\frac {\gamma +\alpha }{2}}}}={\frac {\mathrm {tg} \,{\frac {\gamma -\alpha }{2}}}{\mathrm {cotg} \,{\frac {\beta }{2}}}}}$

Pozri aj

• Tangens
• Sínusová veta
• Kosínusová veta
• Goniometria