Update NA21B005.tex

jan-may-2022-latex/NA21B005/NA21B005.tex

@@ -1,2 +1,38 @@
-\section{NA21B005}
-Student shall edit this file and include stuff for the assignment
+\documentclass{article}
+\usepackage[margin=1in]{geometry}
+
+
+\title{Euler’s Identity}
+\author{Amar Nath Singh NA21B005}
+\date{June 2022}
+
+\begin{document}
+
+\maketitle
+
+\section{Euler’s Identity}
+\begin{equation}
+    e^{i\pi} + 1 = 0
+\end{equation}
+\\
+A very famous equation, Euler’s identity relates the seemingly random values of pi, e, and the square root of -1. It is considered by many to be the most beautiful equation in mathematics.
+
+A more general formula is
+
+\begin{equation}
+    e^{i x} = \cos x + i \sin x
+\end{equation}
+\\
+When x = $\pi$ , the value of $\cos$ x & is -1, while  i$\sin x$  is 0, resulting in Euler’s identity, as -1 + 1 = 0.\\ \\
+\begin{center}
+\begin{tabular}{ |l|l| } 
+ \hline
+ $\pi$ & The number $\pi$ is a mathematical constant that is approximately equal to 3.14159. \\  
+ $e$ & It is the base of the natural logarithms, approximately equal to 2.71828.\\
+ $i$ & The value of i is $\sqrt{-1}$.\\
+ $\cos$ & cosine are trigonometric functions of an angle.\\
+ $\sin$ & sine are trigonometric functions of an angle.\\
+ \hline
+\end{tabular}
+\end{center}
+\end{document}