% ReeTutorsMath.org
% Last Updated 2015 Jan 13

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\chead{1 Page of Trigonometry Formulas by www.ReeTutorsMath.org}
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\begin{document}
\centering

\subsection*{Pythagorean Identities}
\begin{equation*}
\begin{array}{r c l}
\sin^2(\theta) +  \cos^2(\theta) & = &1 \\
\noalign{\medskip}
\tan^2(\theta) + 1               & = & \sec^2(\theta)\\
\noalign{\medskip}
1              + \cot^2(\theta)  &=& \csc^2(\theta) \\
\noalign{\medskip}
\end{array}
\end{equation*}


\subsection*{Power Reducing Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin^2(\theta) & =& \displaystyle \frac{1-\cos(2\theta)}{2}\\
\noalign{\medskip}
\cos^2(\theta) & =& \displaystyle \frac{1+\cos(2\theta)}{2}\\
\noalign{\medskip}
\tan^2(\theta) & =& \displaystyle \frac{1-\cos(2\theta)}{1+\cos(2\theta)}\\
\noalign{\medskip}
\end{array}
\end{equation*}

\subsection*{Double-Angle Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin(2\theta)&=& 2\sin(\theta)\cos(\theta)\\
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\cos(2\theta)&=& \cos^2(\theta)-\sin^2(\theta)\\
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\cos(2\theta)&=& 2\cos^2(\theta)-1\\
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\cos(2\theta)&=& 1-2\sin^2(\theta)\\
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\tan(2\theta)&=& \displaystyle \frac{2\tan(\theta)}{1-\tan^2(\theta)}\\
\end{array}
\end{equation*}

\subsection*{Half-Angle Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin\left( \displaystyle \frac{\theta}{2}\right) &=& ^+_- \sqrt{ \displaystyle \frac{1-\cos(\theta)}{2}}\\
\noalign{\medskip}
\cos\left( \displaystyle \frac{\theta}{2}\right) &=& ^+_- \sqrt{ \displaystyle \frac{1+\cos(\theta)}{2}}\\
\noalign{\medskip}
\tan\left( \displaystyle \frac{\theta}{2}\right) &=& \displaystyle \frac{1-\cos(\theta)}{\sin(\theta)}\\
\noalign{\medskip}
\tan\left( \displaystyle \frac{\theta}{2}\right) &=& \displaystyle \frac{\sin(\theta)}{1+\cos(\theta)}\\
\end{array}
\end{equation*}

\subsection*{Sum and Difference Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin(A+B) &=& \sin(A)\cos(B) + \cos(A)\sin(B)\\
\noalign{\medskip}
\sin(A-B) &=& \sin(A)\cos(B) - \cos(A)\sin(B)\\
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\cos(A+B) &=& \cos(A)\cos(B) - \sin(A)\sin(B)\\
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\cos(A-B) &=& \cos(A)\cos(B) + \sin(A)\sin(B)\\
\\
\tan(A+B) &=& \displaystyle \frac{\tan(A)+\tan(B)}{1-\tan(A)\tan(B)}\\
\\
\tan(A-B) &=& \displaystyle \frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}\\
\\
\\
\end{array}
\end{equation*}

\subsection*{Product-to-Sum Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin(A)\sin(B) &=& \displaystyle \frac{1}{2} [\cos(A-B)-\cos(A+B)]\\
\\
\cos(A)\cos(B) &=& \displaystyle\frac{1}{2} [\cos(A-B)+\cos(A+B)]\\
\\
\sin(A)\cos(B) &=& \displaystyle\frac{1}{2} [\sin(A-B)+\sin(A+B)]\\
\\
\\
\end{array}
\end{equation*}

\subsection*{Sum-to-Product Formulas}
\begin{equation*}
\begin{array}{r c l}
\sin(A)+\sin(B) &=& 2\sin\left(\displaystyle \frac{A+B}{2}\right)\cos\left(\displaystyle \frac{A-B}{2}\right)\\
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\sin(A)-\sin(B) &=& 2\cos\left(\displaystyle \frac{A+B}{2}\right)\sin\left(\displaystyle \frac{A-B}{2}\right)\\
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\cos(A)+\cos(B) &=& 2\cos\left(\displaystyle \frac{A+B}{2}\right)\cos\left(\displaystyle \frac{A-B}{2}\right)\\
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\cos(A)-\cos(B) &=& - 2\sin\left(\displaystyle \frac{A+B}{2}\right)\sin\left(\displaystyle \frac{A-B}{2}\right)\\
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\end{array}
\end{equation*}


\end{document}
