Question

Cum se rezlova:
$2 \sin { }^{3} (x) + 3 \cos(x) \times \sin {}^{2} (x) - \sin(x) \times \cos {}^{2} (x) - \cos {}^{3} (x)$
Trebuie sa ajung la ecuatia omogena in sinus si cosinus si nu stiu cum

Answer 1

[tex]2\cdot \sin^3 x+3\cdot \cos x\cdot \sin^2 x-\sin x\cdot \cos^2 x-\cos^3 x=0\\ \text{Impartind toata ecuatia la}\ \cos^3 x\neq 0:\\ 2\cdot \dfrac{\sin^3 x}{\cos^3 x}+3\cdot \dfrac{\sin^2 x}{\cos^2 x}-\dfrac{\sin x}{\cos x}-1=0\\ \\ 2\cdot tg^3 x+3\cdot tg^2x -tg\ x-1=0\\ \text{Notam:}tg\ x=t:\\ 2t^3+3t^2-t-1=0\\ \text{Nu e usor de ghicit,dar aceasta se descompune asa:}\\ (2t+1)(t^2+t-1)=0\\ \text{Mai departe egalezi fiecare paranteza cu 0 si afli solutiile.}[/tex]