Question

Mă puteți ajuta? Am nevoie de rezolvarea acestui ex.. Mulțumesccc

Determinati toate nr reale x∈ [0, pi] , pentru care : (sin x +2cosx)/3 =sin x.

Answer 1

   
[tex]\displaystyle\\ \frac{\sin x +2\cos x}{3} =\sin x ~~~\Big| \cdot 3 \\\\ \sin x + 2\cos x = 3\sin x\\\\ 2\cos x = 3\sin x - \sin x\\\\ 2\cos x = 2\sin x ~~~\Big| : 2 \\\\ \cos x = \sin x~~~\Big| : \sin x\\\\ \frac{\cos x}{\sin x} = 1\\\\ \text{ctg}\,x = 1 \\\\ x = \text{arcctg}(1) = \boxed{\bf \frac{\pi}{4} } = \boxed{\bf 45^o} \in [0; \pi][/tex]