Solve xcosθ=1

$$x \cos \theta = 1$$

Solve for x

$$x=\frac{1}{\cos(\theta )}$$

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

Steps for Solving Linear Equation

The equation is in standard form.

$$\cos(\theta )x=1$$

Divide both sides by \cos(\theta ).

$$\frac{\cos(\theta )x}{\cos(\theta )}=\frac{1}{\cos(\theta )}$$

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

$$x=\frac{1}{\cos(\theta )}$$

Solve for θ

$$\theta =-\arccos(\frac{1}{x})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\arccos(\frac{1}{x})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|x|\geq 1$$