{l}{y=cos(2x)}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b} хәл итегез

$$\left. \begin{array} { l } { y = \cos(2 x) }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

x, y, z өчен чишелеш (complex solution)

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

$$x=-\frac{i\ln(\sqrt{c^{2}-1}+c)}{2}+\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }y=c\text{, }z=c\text{, }a=c\text{ and }b=c$$

x, y, z өчен чишелеш

$$x=\frac{\arccos(b)+2\pi n_{1}}{2}\text{, }n_{1}\in \mathrm{Z}\text{, }y=b\text{, }z=b$$

$$x=\frac{-\arccos(b)+2\pi n_{2}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }y=b\text{, }z=b\text{, }c=b\text{ and }a=b\text{ and }|b|\leq 1$$