Question

sin2x+1=cosx+2sin решите уравнение дам 40б

Answer 1

Sin2x + 1 = Cosx + 2Sinx

Sin2x - 2Sinx + 1 - Cosx = 0

(2SinxCosx - 2Sinx) + (1 - Cosx) = 0

2Sinx(Cosx - 1) - (Cosx - 1) = 0

(Cosx - 1)(2Sinx - 1) = 0

$\left[\begin{array}{ccc}Cosx-1=0\\2Sinx-1=0\end{array}\right\\\\\\\left[\begin{array}{ccc}Cosx=1\\Sinx=\frac{1}{2} \end{array}\right\\\\\\\left[\begin{array}{ccc}x=2\pi n,n\in Z \\x=(-1)^{n}arcSin\frac{1}{2}+\pi n,n\in Z   \end{array}\right\\\\\\\left[\begin{array}{ccc}x=2\pi n,n\jn Z \\x=(-1)^{n}\frac{\pi }{6}+\pi n,n\in Z   \end{array}\right$