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

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

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

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

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

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

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