Question

Find
the General Solution to the equation
2 cos²x + 3 sin X =0​

Answer 1

Answer:

$2(1 - {sin}^{2} x) + 3 \sin(x) = 0 \\ \\ 2 - 2 {sin}^{2} x + 3 \sin(x) = 0 \\ \\ 2 {sin}^{2} x - 3 \sin(x) - 2 = 0 \\ \\ 2 {sin}^{2} x - 4sinx + sinx - 2 = 0 \\ \\ 2sinx(sinx - 2) + 1(sinx - 2) = 0 \\ \\ (2sinx + 1)(sinx - 2) = 0 \\ \\ sinx = 2 \: \: is \: not \: possiable \\ \\ sinx = - \frac{1}{2} \\ \\ sinx = sin( \frac{5\pi}{6} ) \\ \\ x = n\pi + ({ - 1})^{n} ( \frac{5\pi}{6}$