{l}{x=sin^3t/sqrt{cos2t}quady=cos^3t/sqrt{cos2t}}{dy/dx=?} шешу

$$\left. \begin{array} { l } { x = \frac { \sin ^ { 3 } t } { \sqrt { \cos 2 t } } \quad y = \frac { \cos ^ { 3 } t } { \sqrt { \cos 2 t } } } \\ { \frac { d y } { d x } = ? } \end{array} \right.$$

x мәнін табыңыз (complex solution)

$$x=y\left(\cos(2t)\right)^{-\frac{1}{2}}\left(\sin(t)\right)^{3}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{1}}{2}+\frac{\pi }{4}$$

x мәнін табыңыз

$$\left\{\begin{matrix}x=\frac{y\left(\sin(t)\right)^{3}}{\sqrt{\cos(2t)}}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }\left(t>\pi n_{3}+\frac{3\pi }{4}\text{ and }t<\pi n_{3}+\frac{5\pi }{4}\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }t=\frac{\pi n_{2}}{2}+\frac{\pi }{4}\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(t\geq \pi n_{1}-\frac{\pi }{4}\text{ and }t\leq \pi n_{1}+\frac{\pi }{4}\right)\text{ and }\exists n_{4}\in \mathrm{Z}\text{ : }\left(t>\pi n_{4}-\frac{\pi }{4}\text{ and }t<\pi n_{4}+\frac{\pi }{4}\right)\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }\left(t>\pi n_{3}+\frac{3\pi }{4}\text{ and }t<\pi n_{3}+\frac{5\pi }{4}\right)\end{matrix}\right.$$