Question

решите уравнение 5/sin^2 X

Answer 1

$frac{5}{ sin {}^{2} (x) } - frac{3}{ sin(x) } - 2 = 0 \ frac{5 - 3 sin(x) - 2 sin {}^{2} (x) }{ sin(x) } = 0 \ sin(x) ≠0 \ x≠pi : k : \ - 2 sin {}^{2} (x) - 3 sin(x) + 5 = 0/ times ( - 1) \ 2 sin {}^{2} (x) + 3 sin(x) - 5 = 0 \ sin(x) = t : : : - 1 leqslant t leqslant 1 \ 2 {t}^{2} + 3t - 5 = 0 \ x = frac{ -3 ± sqrt{9 + 4 times 5 times 2} }{4} = frac{ - 3±7}{4} = - frac{5}{2} ;1 \ sin(x) = 1 \ x = frac{pi}{2} + 2pi : k :; kinmathbb Z$
$pi leqslant frac{pi}{2} + 2pi : k leqslant frac{5pi}{2} \ frac{pi}{2} leqslant 2pi : k leqslant 2pi \ frac{1}{4} leqslant k leqslant 1 \ k = 1 \ frac{pi}{2} + 2pi = frac{5pi}{2}$