Solve y=axccos2x

$$y = a x c \cos 2 x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{y}{cx\cos(2x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ and }x\neq 0\text{ and }c\neq 0\\a\in \mathrm{C}\text{, }&\left(c=0\text{ or }x=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$axc\cos(2x)=y$$

The equation is in standard form.

$$cx\cos(2x)a=y$$

Divide both sides by xc\cos(2x).

$$\frac{cx\cos(2x)a}{cx\cos(2x)}=\frac{y}{cx\cos(2x)}$$

Dividing by xc\cos(2x) undoes the multiplication by xc\cos(2x).

$$a=\frac{y}{cx\cos(2x)}$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{y}{ax\cos(2x)}\text{, }&a\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ and }x\neq 0\\c\in \mathrm{C}\text{, }&\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ or }a=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$axc\cos(2x)=y$$

The equation is in standard form.

$$ax\cos(2x)c=y$$

Divide both sides by ax\cos(2x).

$$\frac{ax\cos(2x)c}{ax\cos(2x)}=\frac{y}{ax\cos(2x)}$$

Dividing by ax\cos(2x) undoes the multiplication by ax\cos(2x).

$$c=\frac{y}{ax\cos(2x)}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{y}{cx\cos(2x)}\text{, }&c\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ or }c=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$axc\cos(2x)=y$$

The equation is in standard form.

$$cx\cos(2x)a=y$$

Divide both sides by xc\cos(2x).

$$\frac{cx\cos(2x)a}{cx\cos(2x)}=\frac{y}{cx\cos(2x)}$$

Dividing by xc\cos(2x) undoes the multiplication by xc\cos(2x).

$$a=\frac{y}{cx\cos(2x)}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{y}{ax\cos(2x)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ and }x\neq 0\text{ and }a\neq 0\\c\in \mathrm{R}\text{, }&\left(\exists n_{1}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{1}}{2}+\frac{\pi }{4}\text{ or }x=0\text{ or }a=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$axc\cos(2x)=y$$

The equation is in standard form.

$$ax\cos(2x)c=y$$

Divide both sides by ax\cos(2x).

$$\frac{ax\cos(2x)c}{ax\cos(2x)}=\frac{y}{ax\cos(2x)}$$

Dividing by ax\cos(2x) undoes the multiplication by ax\cos(2x).

$$c=\frac{y}{ax\cos(2x)}$$