Leysa (xy)^-14sin4θ-1=sqrt{5}

$$( x y ) ^ { - 1 } 4 \sin 4 \theta - 1 = \sqrt { 5 }$$

Leystu fyrir x (complex solution)

$$x=-\frac{\left(1-\sqrt{5}\right)\sin(4\theta )}{y}$$

$$y\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{4}$$

Leystu fyrir y (complex solution)

$$y=-\frac{\left(1-\sqrt{5}\right)\sin(4\theta )}{x}$$

$$x\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{4}$$

Leystu fyrir x

$$x=-\frac{\left(1-\sqrt{5}\right)\sin(4\theta )}{y}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta >\frac{\pi n_{1}}{4}\text{ and }\theta <\frac{\pi n_{1}}{4}+\frac{\pi }{4}\right)\text{ and }y\neq 0$$

Leystu fyrir y

$$y=-\frac{\left(1-\sqrt{5}\right)\sin(4\theta )}{x}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta >\frac{\pi n_{1}}{4}\text{ and }\theta <\frac{\pi n_{1}}{4}+\frac{\pi }{4}\right)\text{ and }x\neq 0$$