Solve sin2x=asinx

$$\sin 2 x = a \sin x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=2\cos(x)\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\\a\in \mathrm{C}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\sin(x)=\sin(2x)$$

The equation is in standard form.

$$\sin(x)a=\sin(2x)$$

Divide both sides by \sin(x).

$$\frac{\sin(x)a}{\sin(x)}=\frac{\sin(2x)}{\sin(x)}$$

Dividing by \sin(x) undoes the multiplication by \sin(x).

$$a=\frac{\sin(2x)}{\sin(x)}$$

Divide \sin(2x) by \sin(x).

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

Solve for a

$$\left\{\begin{matrix}\\a=2\cos(x)\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\sin(x)=\sin(2x)$$

The equation is in standard form.

$$\sin(x)a=\sin(2x)$$

Divide both sides by \sin(x).

$$\frac{\sin(x)a}{\sin(x)}=\frac{\sin(2x)}{\sin(x)}$$

Dividing by \sin(x) undoes the multiplication by \sin(x).

$$a=\frac{\sin(2x)}{\sin(x)}$$

Divide \sin(2x) by \sin(x).

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

Solve for x

$$\left\{\begin{matrix}\\x=\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\text{unconditionally}\\x=-\arccos(\frac{a}{2})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{; }x=\arccos(\frac{a}{2})+2\pi n_{3}\text{, }n_{3}\in \mathrm{Z}\text{, }&|a|\leq 2\end{matrix}\right.$$