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-#+TITLE:Trigonometric identities
-#+SETUPFILE: ../math_options.org
-#+LATEX_HEADER: \usepackage{bm}
-#+LATEX_HEADER: \usepackage{mathtools}
-
-* Disclaimer
-This site as of now just a technology demonstration and its claims
-should not be taken as true (even though I myself am pretty confident
-they are)
-
-* Pythagorean identities
-\begin{align*}
-&\cos^2\left(x\right) + \sin^2\left(x\right) = 1\\
-&\tan^2\left(x\right) + 1                    = \sec^2\left(x\right)\\
-&1                    + \cot^2\left(x\right) = \csc^2\left(x\right)
-\end{align*}
-* Sum of angles
-\begin{align*}
-&\sin\left(a \pm b\right) = \sin\left(a\right)\cos\left(b\right) \pm \cos\left(a\right)\sin\left(b\right)\\
-&\cos\left(a \pm b\right) = \cos\left(a\right)\cos\left(b\right) \mp \sin\left(a\right)\sin\left(b\right)\\
-&\tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a) \tan(b)}
-\end{align*}
-* Multiple angles
-\begin{align*}
-&\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\
-&\cos(2\theta) = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta
-\end{align*}
-* Half-angle formulae
-\begin{align*}
-&\sin \frac{\theta}{2} = \pm \sqrt{\frac{1-\cos\theta}{2}}\\
-&\cos \frac{\theta}{2} = \pm \sqrt{\frac{1+\cos\theta}{2}}
-\end{align*}
-* Power-reduction formulae
-\begin{align*}
-&\sin^2\theta = \frac{1 - \cos(2\theta)}{2}\\
-&\cos^2\theta = \frac{1 + \cos(2\theta)}{2}
-\end{align*}
-* Product-to-sum formulae
-\begin{align*}
-&2 \cos\theta \cos\varphi = \cos(\theta-\varphi) + \cos(\theta+\varphi)\\
-&2 \sin\theta \sin\varphi = \cos(\theta-\varphi) - \cos(\theta+\varphi)\\
-&2 \sin\theta \cos\varphi = \sin(\theta+\varphi) + \sin(\theta-\varphi)\\
-&2\cos\theta\sin\varphi = \sin(\theta+\varphi) - \sin(\theta-\varphi)
-\end{align*}
-* Sum-to-product formulae
-\begin{align*}
-&\sin\theta \pm \sin\varphi = 2 \sin\left(\frac{\theta\pm\varphi}{2}\right) \cos\left(\frac{\theta\mp\varphi}{2}\right)\\
-&\cos\theta + \cos\varphi = 2 \cos\left(\frac{\theta+\varphi}{2}\right) \cos\left(\frac{\theta-\varphi}{2}\right)\\
-&\tan\theta \pm \tan\varphi = \frac{\sin(\theta\pm\varphi)}{\cos\theta \cos\varphi}\\
-&\cos\theta - \cos\varphi = - 2 \sin\left(\frac{\theta+\varphi}{2}\right) \sin\left(\frac{\theta-\varphi}{2}\right)
-\end{align*}