Lahenda (sinθ)(tanθ)(sinθ)(x)=1

$$( \sin \theta ) ( \tan \theta ) ( \sin \theta ) ( x ) = 1$$

Lahendage ja leidke x (complex solution)

$$x=-\frac{4\cos(\theta )}{\sin(3\theta )-3\sin(\theta )}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}\text{ and }2\left(\sin(3\theta )-3\sin(\theta )\right)\neq 0$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage \sin(\theta ) ja \sin(\theta ), et leida \left(\sin(\theta )\right)^{2}.

$$\left(\sin(\theta )\right)^{2}\tan(\theta )x=1$$

Võrrand on standardkujul.

$$\tan(\theta )\left(\sin(\theta )\right)^{2}x=1$$

Jagage mõlemad pooled \left(\sin(\theta )\right)^{2}\tan(\theta )-ga.

$$\frac{\tan(\theta )\left(\sin(\theta )\right)^{2}x}{\tan(\theta )\left(\sin(\theta )\right)^{2}}=\frac{1}{\tan(\theta )\left(\sin(\theta )\right)^{2}}$$

\left(\sin(\theta )\right)^{2}\tan(\theta )-ga jagamine võtab \left(\sin(\theta )\right)^{2}\tan(\theta )-ga korrutamise tagasi.

$$x=\frac{1}{\tan(\theta )\left(\sin(\theta )\right)^{2}}$$

Jagage 1 väärtusega \left(\sin(\theta )\right)^{2}\tan(\theta ).

$$x=\frac{\cot(\theta )}{\left(\sin(\theta )\right)^{2}}$$

Lahendage ja leidke x

$$x=\frac{\cot(\theta )}{\left(\sin(\theta )\right)^{2}}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta >\frac{\pi n_{1}}{2}\text{ and }\theta <\frac{\pi n_{1}}{2}+\frac{\pi }{2}\right)$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage \sin(\theta ) ja \sin(\theta ), et leida \left(\sin(\theta )\right)^{2}.

$$\left(\sin(\theta )\right)^{2}\tan(\theta )x=1$$

Võrrand on standardkujul.

$$\tan(\theta )\left(\sin(\theta )\right)^{2}x=1$$

Jagage mõlemad pooled \left(\sin(\theta )\right)^{2}\tan(\theta )-ga.

$$\frac{\tan(\theta )\left(\sin(\theta )\right)^{2}x}{\tan(\theta )\left(\sin(\theta )\right)^{2}}=\frac{1}{\tan(\theta )\left(\sin(\theta )\right)^{2}}$$

\left(\sin(\theta )\right)^{2}\tan(\theta )-ga jagamine võtab \left(\sin(\theta )\right)^{2}\tan(\theta )-ga korrutamise tagasi.

$$x=\frac{1}{\tan(\theta )\left(\sin(\theta )\right)^{2}}$$

Jagage 1 väärtusega \left(\sin(\theta )\right)^{2}\tan(\theta ).

$$x=\frac{\cot(\theta )}{\left(\sin(\theta )\right)^{2}}$$