Solve 1-cosx=sqrt{3}si

$$1 - \cos x = \sqrt { 3 } s i$$

Solve for s

$$s=-\frac{\sqrt{3}i\left(-\cos(x)+1\right)}{3}$$

Steps for Solving Linear Equation

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

$$i\sqrt{3}s=1-\cos(x)$$

The equation is in standard form.

$$\sqrt{3}is=-\cos(x)+1$$

Divide both sides by i\sqrt{3}.

$$\frac{\sqrt{3}is}{\sqrt{3}i}=\frac{-\cos(x)+1}{\sqrt{3}i}$$

Dividing by i\sqrt{3} undoes the multiplication by i\sqrt{3}.

$$s=\frac{-\cos(x)+1}{\sqrt{3}i}$$

Divide 1-\cos(x) by i\sqrt{3}.

$$s=\frac{\sqrt{3}\left(i\cos(x)-i\right)}{3}$$

Solve for x

$$x=\left(-i\right)\ln(1+\left(-i\right)\times 3^{\frac{1}{2}}s+\left(-1\right)\times 3^{\frac{1}{4}}\left(\left(-1\right)s\left(3^{\frac{1}{2}}s+2i\right)\right)^{\frac{1}{2}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\left(-i\right)\ln(1+\left(-i\right)\times 3^{\frac{1}{2}}s+3^{\frac{1}{4}}\left(\left(-1\right)s\left(3^{\frac{1}{2}}s+2i\right)\right)^{\frac{1}{2}})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$