Question

Помогите пожалуйста алгебра 10 класс
Решить уравнение
5-7sin(x)=3cos^2(x)

Answer 1

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