Question

Supondo que 0° ≤x ≤ 360°, resolva a equacao cos2x -4 cos x +3=0

Answer 1

Vamos usar arco duplo o cosseno :

$\text{cos(2x)} = 2\text{cos}^2(\text x)-1$

Temos :

$\text{cos(2x)}-4\text{cos(x)}+3=0 \\\\ 2\text{cos}^2(\text x)-1-4\text{cos(x)}+3=0 \\\\ 2\text{cos}^2(\text x)-4\text{cos(x)}+2=0 \\\\ \text{cos}^2(\text x)-2\text{cos(x)}+1=0 \\\\ \ [\text{cos(x)}-1]^2=0\\\\\ \text{cos(x)} - 1 = 0 \\\\ \text{cos(x)}=1 \\\\ \huge\boxed{\text x = 0^\circ \ \ \text{ou} \ \ \text{x}=360^\circ }\checkmark$