1\\ \sin x = \frac{9 -\sqrt{65}}{8}\\ x = \arcsin{(\frac{9 -\sqrt{65}}{8})} " alt="4\cos^2 x +9 \sin x = 5\\ 4-4\sin^2 x +9 \sin x = 5\\ 4\sin^2 x - 9 \sin x +1 = 0\\ D = \sqrt{(81 - 16)} = \sqrt{65}\\ \sin x_{1,2} = \frac{9 \pm \sqrt{65}}{8}\\ \frac{9 +\sqrt{65}}{8}>1\\ \sin x = \frac{9 -\sqrt{65}}{8}\\ x = \arcsin{(\frac{9 -\sqrt{65}}{8})} " align="absmiddle" class="latex-formula">