Question

Determinați x aparține (0, pi/2), știind că 3sin x-2cos x/ cos x= 1.

Answer 1

   
[tex]\displaystyle \frac{3\sin x -2\cos x}{\cos x}=1 \\ \\ \frac{3\sin x}{\cos x} - \frac{2\cos x}{\cos x}=1 \\ 3\,\text{tg}\, x - 2 = 1 \\ 3\,\text{tg}\, x = 1 +2\\ 3\,\text{tg}\, x = 3 \\ \text{tg}\,x = 1 \\ x = arctg(1) = \boxed{45^o}[/tex]