$\tan\left(x\right)-1=\frac{\sin\left(x\right)^2-\cos\left(x\right)^2}{\sin\left(x\right)\cos\left(x\right)+\cos\left(x\right)^2}$

$\frac{1-sinx}{cosx}=\frac{cosx}{1+sinx}$

$tan\left(x\right)+cot\left(x\right)=sec\left(x\right)cosec\left(x\right)$

$\frac{1+\cos2x}{\sin2x}=\cot x$

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

$\tan\left(a\right)+\cot\left(a\right)=\sec\left(a\right)\csc\left(a\right)$

$\sec x-\sin x\tan x=\cos x$