Question

demonstrati ca sin la a doua+cos la a doua=1​

Answer 1

 

Vom folosi triunghiul dreptunghic din imaginea atasata.

$\displaystyle\bf\\Folosim~formulele:\\\\1)~~AB^2+AC^2=BC^2~~~(Teorema~lui~Pitagora)\\\\2)~~sinB=\frac{AC}{BC}~~si~~cosB=\frac{AB}{BC}\\\\Rezolvare:\\\\sin^2B+cos^2B=\left(\frac{AC}{BC}\right)^2+\left(\frac{AB}{BC}\right)^2=\\\\=\frac{AC^2}{BC^2}+\frac{AB^2}{BC^2}=\frac{AB^2+AC^2}{BC^2}=\frac{BC^2}{BC^2}=1$