Question

Arătați că sin(pi-x)+sin(pi+x)=0,pentru orice numar real x

Answer 1

Stim ca in general
$\sin{(a-b)}=\sin{a}\cos{b}-\sin{b}\cos{a}$
$\sin{(a+b)}=\sin{a}\cos{b}+\sin{b}\cos{a}$
Si mai stim ca
$\sin{\pi}=0$
$\cos{\pi}=-1$
Asadar avem
$\sin{(\pi-x)}+\sin{(\pi+x)}=\sin{\pi}\cos{x}-\cos{\pi}\sin{x}+\sin{\pi}\cos{x}+\cos{\pi}\sin{x}=2\sin{\pi}\cos{x}=2*0*\cos{x}=0$