Solve ycosx=cosxsinx

$$y \cos x = \cos x \sin x$$

Solve for y

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

Steps for Solving Linear Equation

The equation is in standard form.

$$\cos(x)y=\frac{1}{2}\sin(2x)$$

Divide both sides by \cos(x).

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

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

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

Divide \frac{1}{2}\sin(2x) by \cos(x).

$$y=\sin(x)$$

Solve for x

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