This is just a quick summary of the trig identities. I will be adding to it, but right now, this is what is needed to go with the integration by trigonometric substitution page.
\large \mathrm{\sin^2x + \cos^2x = 1}
\\ \: \\ \mathrm{1 + \tan^2x = \sec^2 x}
\\ \: \\ \mathrm{\sin(x \pm y) = \sin x \cos y \pm \cos x \sin y }
\\ \: \\ \mathrm{\cos(x \pm y) = \cos x \cos y \mp \sin x \sin y }
\\ \: \\ \mathrm{\tan(x \pm y) = \dfrac{\tan x \pm \tan y}{1 \mp \tan x \tan y}}
\\ \: \\ \mathrm{\sin(2x) = 2 \sin x \cos x}
\\ \: \\ \mathrm{\cos(2x) = \cos^2(x) - \sin^2(x)}
\\ \: \\ \mathrm{\sin^2(x) = \dfrac{1 - \cos(2x)}{2}}
\\ \: \\ \mathrm{\cos^2(x) = \dfrac{1 + \cos(2x)}{2}}
\\ \: \\ \mathrm{\sin(-x) = -\sin(x)}
\\ \: \\ \mathrm{\cos(-x) = \cos(x)}