Question

Se consideră triunghiul dreptunghic ABC, cu ipotenuza AB . Demonstrați că cos A cos B = sin A sin B

Answer 1

cosAcosB = sinAsinB

AC/AB×BC/AB = BC/AB×AC/AB

AC×BC/AB² = AC×BC/AB²

q.e.d.

Answer 2

$\it \Delta CAB-dreptunghic,\ \ m(\hat C)=90^o\\ \\ cosA=sin(90^o-A)=sinB\ \ \ \ \ (1)\\ \\ cosB=sin(90^o-B)=sinA\ \ \ \ \ (2)\\ \\ (1),\ (2)\ \Rightarrow\ cosAcosB=sinBsinA\ \Rightarrow\ cosAcosB=sinAsinB$