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Added ME22B142 #156

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Delete me22b142.tex
kanupriyavirdi Feb 12, 2023
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Added ME22B142
kanupriyavirdi Feb 12, 2023
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12 changes: 12 additions & 0 deletions me22b142.tex
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\section{ME22B142}
\subsection{Sum of Sines}
\begin{equation}
\sum_{n=1}^{n} sin(\alpha+(i-1)\beta) = \frac{sin(\alpha+\frac{(n-1)\beta}{2})sin(\frac{n\beta}{2})}{sin(\frac{\beta}{2})}
\end{equation}
This expression is derived from a much simpler and general summation of 2 sines.
\begin{equation}
sinA + sinB = 2sin(\frac{A+B}{2})cos(\frac{A-B}{2})
\end{equation}
These formulae are used almost all the time when finding solutions of triangles, a major part of the JEE Advanced examination. A very beautiful relation indeed because such a big trigonometric sum can be written in such a short format. I looked up the equation when studying for JEE in NCERT. \footnote{\href{https://ncert.nic.in/textbook.php?kemh1=3-16}{NCERT Book link on NCERT Website}}

Name- Kanupriya Virdi | Roll number- ME22B142 | GitHub user ID- kanupriyavirdi