Question

Решить уравнение 3cos^2 x + 7sinx – 5 = 0

Answer 1

$3Cos^{2}x+7Sinx-5=0\\\\3(1-Sin^{2}x)+7Sinx-5=0\\\\3-3Sin ^{2}x+7Sinx-5=0\\\\3Sin^{2}x-7Sinx+2=0\\\\Sinx=m \ ; \ -1\leq m \leq1\\\\3m^{2}-7m+2=0\\\\D=(-7)^{2}-4*3*2=49-24=25=5^{2}\\\\m_{1} =\frac{7-5}{6}=\frac{1}{3}\\\\m_{2} =\frac{7+5}{6}=2-neyd\\\\Sinx=\frac{1}{3}\\\\\boxed{x=(-1)^{n}arc Sin\frac{1}{3}+\pi n,n\in Z}$