Solve cos(θ)=xcos(180-θ)

$$\cos ( \theta ) =x \cos ( 180- \theta )$$

Solve for x (complex solution)

$$x=\frac{2\cos(\theta )e^{180i-i\theta }}{\left(e^{-i\theta +180i}\right)^{2}+1}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}-\frac{113\pi }{2}+180$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x\cos(180-\theta )=\cos(\theta )$$

The equation is in standard form.

$$\cos(180-\theta )x=\cos(\theta )$$

Divide both sides by \cos(180-\theta ).

$$\frac{\cos(180-\theta )x}{\cos(180-\theta )}=\frac{\cos(\theta )}{\cos(180-\theta )}$$

Dividing by \cos(180-\theta ) undoes the multiplication by \cos(180-\theta ).

$$x=\frac{\cos(\theta )}{\cos(180-\theta )}$$

Solve for x

$$x=\frac{\cos(\theta )}{\sin(180)\sin(\theta )+\cos(180)\cos(\theta )}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}-\frac{113\pi }{2}+180$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x\cos(180-\theta )=\cos(\theta )$$

The equation is in standard form.

$$\cos(180-\theta )x=\cos(\theta )$$

Divide both sides by \cos(180-\theta ).

$$\frac{\cos(180-\theta )x}{\cos(180-\theta )}=\frac{\cos(\theta )}{\cos(180-\theta )}$$

Dividing by \cos(180-\theta ) undoes the multiplication by \cos(180-\theta ).

$$x=\frac{\cos(\theta )}{\cos(180-\theta )}$$