Question

3.senx - 4.sen^3x = 1/2

Answer 1

$\displaystyle \sf \underline{\text{Arco Triplo da fun{\c c}{\~a}o Seno}}:\\\\ sen(3x) = 3sen(x)-4sen^3(x) \\\\\\ Da{\'i}}, \ temos: \\\\ 3sen(x)-4sen^3(x)=\frac{1}{2} \\\\\\ sen(3x) = \frac{1}{2} \\\\\\ sen(3x) = sen\left(\frac{\pi}{6}+2\cdot k\cdot \pi \right) \\\\\\ 3x = \frac{\pi}{6}+2\cdot k\cdot \pi \\\\\\ \boxed{\sf \ x = \frac{\pi }{18}+\frac{2\cdot k\cdot \pi}{3} \ \ \ ; \ \ k\in\mathbb{Z} \ }\checkmark$