y=cos(x^2) хәл итегез

$$y = \cos ( x ^ { 2 } )$$

x өчен чишелеш (complex solution)

$$x=\left(-1\right)\left(\left(-i\right)\ln(y+\left(-1\right)\left(y^{2}-1\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(\left(-i\right)\ln(y+\left(-1\right)\left(y^{2}-1\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-1\right)\left(\left(-i\right)\ln(y+\left(y^{2}-1\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}$$

$$x=\left(\left(-i\right)\ln(y+\left(y^{2}-1\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}$$

x өчен чишелеш

$$\left\{\begin{matrix}\\x=\sqrt{-\arccos(y)+2\pi n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(n_{2}>-1\text{ and }y=1\right)\text{; }x=-\sqrt{-\arccos(y)+2\pi n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }\left(n_{2}\geq 1\text{ and }|y|\leq 1\right)\text{ or }\left(n_{2}>-1\text{ and }y=1\right)\text{, }&\text{unconditionally}\\x=-\sqrt{\arccos(y)+2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0\text{; }x=\sqrt{\arccos(y)+2\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }n_{1}\geq 0\text{, }&|y|\leq 1\end{matrix}\right.$$

y өчен чишелеш

$$y=\cos(x^{2})$$