Solve zcosalpha=4sinalpha

$$z \cos \alpha = 4 \sin \alpha$$

Solve for z

$$z=4\tan(\alpha )$$

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

Steps for Solving Linear Equation

The equation is in standard form.

$$\cos(\alpha )z=4\sin(\alpha )$$

Divide both sides by \cos(\alpha ).

$$\frac{\cos(\alpha )z}{\cos(\alpha )}=\frac{4\sin(\alpha )}{\cos(\alpha )}$$

Dividing by \cos(\alpha ) undoes the multiplication by \cos(\alpha ).

$$z=\frac{4\sin(\alpha )}{\cos(\alpha )}$$

Divide 4\sin(\alpha ) by \cos(\alpha ).

$$z=4\tan(\alpha )$$

Solve for α

$$\alpha =\pi n_{1}+\arcsin(\frac{z}{\sqrt{z^{2}+16}})$$

$$n_{1}\in \mathrm{Z}$$