\(\displaystyle \frac{1+\tan^2x}{\tan x}\equiv \sec x\,\csc x.\)

\(\displaystyle \frac{\sin x}{1-\cos^2x}\equiv \csc x.\)

\(\displaystyle \frac{1+\sin x}{1-\sin x}\equiv (\tan x+\sec x)^2.\)

\(\displaystyle \frac{1}{1+\cos x}+\frac{1}{1-\cos x}\equiv 2\csc^2x.\)

\(\displaystyle \frac{\cos x}{1+\sin x}+\frac{\cos x}{1-\sin x}\equiv 2\sec x.\)