Question

Se consideră triunghiul dreptunghic ABC,cu ipotenuza AB.Demonstrați că:
$\cos(a) \cos(b) = \sin(a) \sin(b)$

Answer 1

$\cos(a)\cdot \cos(b) = \sin(a)\cdot\sin(b) \\ \\ \dfrac{cateta~ alaturata~\sphericalangle a}{ipotenuza}\cdot \dfrac{cateta~ alaturata~\sphericalangle b}{ipotenuza} = \\ \\ =\dfrac{cateta~ opusa~\sphericalangle a}{ipotenuza} \cdot \dfrac{cateta~ opusa~\sphericalangle b}{ipotenuza}\\\\ \\ \dfrac{AC}{AB} \cdot \dfrac{CB}{AB} = \dfrac{CB}{AB}\cdot \dfrac{AC}{AB} \\ \\ \dfrac{AC}{AB} \cdot \dfrac{CB}{AB} = \dfrac{AC}{AB}\cdot\dfrac{CB}{AB} \quad (A)$