Solve r=a(1+coss)

$$r = a ( 1 + \cos s )$$

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply a by 1+\cos(s).

$$r=a+a\cos(s)$$

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

$$a+a\cos(s)=r$$

Combine all terms containing a.

$$\left(1+\cos(s)\right)a=r$$

The equation is in standard form.

$$\left(\cos(s)+1\right)a=r$$

Divide both sides by 1+\cos(s).

$$\frac{\left(\cos(s)+1\right)a}{\cos(s)+1}=\frac{r}{\cos(s)+1}$$

Dividing by 1+\cos(s) undoes the multiplication by 1+\cos(s).

$$a=\frac{r}{\cos(s)+1}$$

Solve for r

$$r=a\left(\cos(s)+1\right)$$