Solve p=2acosθ

$$p = 2 a \cos \theta$$

Solve for a

$$\left\{\begin{matrix}a=\frac{p}{2\cos(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\\a\in \mathrm{R}\text{, }&p=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2a\cos(\theta )=p$$

The equation is in standard form.

$$2\cos(\theta )a=p$$

Divide both sides by 2\cos(\theta ).

$$\frac{2\cos(\theta )a}{2\cos(\theta )}=\frac{p}{2\cos(\theta )}$$

Dividing by 2\cos(\theta ) undoes the multiplication by 2\cos(\theta ).

$$a=\frac{p}{2\cos(\theta )}$$

Solve for p

$$p=2a\cos(\theta )$$