基本公式
\(1+\tan ^2 \alpha=\sec^2 \alpha\)
\(1+\cot^2 \alpha = csc^2 \alpha\)
\(\sin {2\alpha} = 2\sin \alpha \cos \alpha\)
\(\cos {2\alpha} = \cos^2 \alpha - \sin^2 \alpha = 2\cos^2 \alpha - 1=1-2\sin^2 \alpha\)
\(\sin^2 \alpha = \dfrac{1-\cos{2\alpha}}{2}\)
\(\cos^2 \alpha = \dfrac{1+\cos{2\alpha}}{2}\)
\(\sin (\alpha + \beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta\)
\(\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha \sin \beta\)
\(\tan(\alpha+\beta)=\dfrac{\tan\alpha+\tan\beta}{1-tan\alpha\cdot\tan\beta}\)
积分公式
\(\displaystyle\int\limits\tan x=-\ln|\cos x|+C\)
\(\displaystyle\int\limits\cot x=\ln|\sin x|+C\)
\(\displaystyle\int\limits\sec x=\ln|\sec x+\tan x|+C\)
\(\displaystyle\int\limits\csc x=\ln|\csc x-\cot x|+C\)
\(\displaystyle\int\limits\sec^2 x=\tan x+C\)
\(\displaystyle\int\limits\csc^2 x=-\cot x+C\)
\(\displaystyle\int\limits\sec x\tan x=\sec x+C\)
\(\displaystyle\int\limits\csc x\cot x=-\csc x+C\)