Solve P=a(1-cosθ)

$$P = a ( 1 - \cos \theta )$$

Solve for a

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

Steps for Solving Linear Equation

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

$$a\left(1-\cos(\theta )\right)=P$$

Use the distributive property to multiply a by 1-\cos(\theta ).

$$a-a\cos(\theta )=P$$

Combine all terms containing a.

$$\left(1-\cos(\theta )\right)a=P$$

The equation is in standard form.

$$\left(-\cos(\theta )+1\right)a=P$$

Divide both sides by 1-\cos(\theta ).

$$\frac{\left(-\cos(\theta )+1\right)a}{-\cos(\theta )+1}=\frac{P}{-\cos(\theta )+1}$$

Dividing by 1-\cos(\theta ) undoes the multiplication by 1-\cos(\theta ).

$$a=\frac{P}{-\cos(\theta )+1}$$

Solve for P

$$P=a\left(-\cos(\theta )+1\right)$$