Solve x=sin^3t/sqrt{cos2t},y=cos^3t/sqrt{cos2t}

$$x = \frac { \sin ^ { 3 } t } { \sqrt { \cos 2 t } } , y = \frac { \cos ^ { 3 } t } { \sqrt { \cos 2 t } }$$

解 x, y (復數求解)

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

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

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

解 x, y

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

$$y=\frac{\left(\cos(t)\right)^{3}}{\sqrt{\cos(2t)}}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(t>\pi n_{1}+\frac{3\pi }{4}\text{ and }t<\pi n_{1}+\frac{5\pi }{4}\right)$$