I am an assistant professor of mathematics at Algean Institute of Mathematics.

My academic interests include complex analysis and analytic number theory.

Converse of Elementary Functions and Their Fundamental Formulas:

First Formula of Radical: $$\boxed{(\sqrt x)^2=x}$$ Second Formula of Radical: $$\boxed{\sqrt{x^2}=\begin{cases} x,~x\ge0\\ -x,~x<0 \end{cases}}$$ First Formula of Cube Root Radical: $$\boxed{(\sqrt[3]x)^3=x}$$ Second Formula of Cube Root Radical: $$\boxed{\sqrt[3]{x^3}=x}$$ First Formula of Logarithm: $$\boxed{2^{\log_2(x)}=x}$$ Second Formula of Logarithm: $$\boxed{\log_2(2^x)=x}$$ First Formula of Arc Sine: $$\boxed{\sin(\operatorname{Arcsin}(x))=x}$$ Second Formula of Arc Sine: $$\boxed{\operatorname{Arcsin}(\sin(x))=\begin{cases} x,~\text{first quadrant}\\ \pi-x,~\text{second and third quadrants}\\ x-2\pi,~\text{fourth quadrant} \end{cases}}$$ First Formula of Arc Cosine: $$\boxed{\cos(\operatorname{Arccos}(x))=x}$$ Second Formula of Arc Cosine: $$\boxed{\operatorname{Arccos}(\cos(x))=\begin{cases} x,~\text{first and second quadrants}\\ 2\pi-x,~\text{third and fourth quadrants} \end{cases}}$$ First Formula of Arc Tangent: $$\boxed{\tan(\operatorname{Arctan}(x))=x}$$ Second Formula of Arc Tangent: $$\boxed{\operatorname{Arctan}(\tan(x))=\begin{cases} x,~\text{first quadrant}\\ x-\pi,~\text{second and third quadrants}\\ x-2\pi,~\text{fourth quadrant} \end{cases}}$$