Solve cos(t)+sin(t)=x*sint

$$\cos ( t ) + \sin ( t ) = x \cdot \sin t$$

Solve for x (complex solution)

$$x=\frac{\left(1-i\right)e^{it}+\left(1+i\right)e^{-it}}{2\sin(t)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }t=\pi n_{1}$$

Steps for Solving Linear Equation

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

$$x\sin(t)=\cos(t)+\sin(t)$$

The equation is in standard form.

$$\sin(t)x=\sin(t)+\cos(t)$$

Divide both sides by \sin(t).

$$\frac{\sin(t)x}{\sin(t)}=\frac{\sin(t)+\cos(t)}{\sin(t)}$$

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

$$x=\frac{\sin(t)+\cos(t)}{\sin(t)}$$

Solve for x

$$x=\frac{\sin(t)+\cos(t)}{\sin(t)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }t=\pi n_{1}$$

Steps for Solving Linear Equation

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

$$x\sin(t)=\cos(t)+\sin(t)$$

The equation is in standard form.

$$\sin(t)x=\sin(t)+\cos(t)$$

Divide both sides by \sin(t).

$$\frac{\sin(t)x}{\sin(t)}=\frac{\sin(t)+\cos(t)}{\sin(t)}$$

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

$$x=\frac{\sin(t)+\cos(t)}{\sin(t)}$$