Question

Daca tgx+ctgx= 5/√3 , calculati sin2x . Multumesc .

Answer 1

Stim urmatoarele
$tgx=\frac{\sin{x}}{\cos{x}}$
$ctgx=\frac{\cos{x}}{\sin{x}}$
$\sin{2x}=2\sin{x}\cos{x}$
Atunci
$\frac{\sin{x}}{\cos{x}}+\frac{\cos{x}}{\sin{x}}=\frac{\sin^{2}{x}+\cos^{2}{x}}{\sin{x}\cos{x}}=\frac{1}{\sin{x}\cos{x}}=\frac{2}{2\sin{x}\cos{x}}=\frac{2}{\sin{2x}}=\frac{5}{\sqrt{3}}\Rightarrow \sin{2x}=\frac{2\sqrt{3}}{5}$