Solve fx=left(cos(x)right)^2-y^2cos(x)

$$fx= { \left( \cos ( x ) \right) }^{ 2 } - { y }^{ 2 } \cos ( x )$$

Solve for f

$$\left\{\begin{matrix}f=\frac{\cos(x)\left(\cos(x)-y^{2}\right)}{x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }|y|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=-y^{2}\cos(x)+\left(\cos(x)\right)^{2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{\cos(x)\left(\cos(x)-y^{2}\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{\cos(x)\left(\cos(x)-y^{2}\right)}{x}$$