Question

tg x +ctg x = 2__sin2x (/)
ajutati va rog!

Answer 1

Stim ca
$\sin{2x}=2\sin{x}\cos{x}$ si
$\sin^{2}{x}+\cos^{2}{x}=1$
Asadar avem urmatoarea relatie
$\frac{2}{\sin{(2x)}}=\frac{2}{2\sin{x}\cos{x}}=\frac{1}{\sin{x}\cos{x}}=\frac{\sin^{2}{x}+\cos^{2}{x}}{\sin{x}\cos{x}}=\frac{\sin^{2}{x}}{\sin{x}\cos{x}}+\frac{\cos^{2}{x}}{\sin{x}\cos{x}}=\frac{\sin{x}}{\cos{x}}+\frac{\cos{x}}{\sin{x}}=tgx+ctgx}$