Prove that: a) $$ \sin x \cdot an x+\cos x=\frac{1}{\cos x} $$ b) $$ \frac{\cos x}{1-\sin x}-\frac{\cos x}{1+\sin x}=2 an x $$

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Prove that: a) $$ \sin x \cdot 	an x+\cos x=\frac{1}{\cos x} $$ b) $$ \frac{\cos x}{1-\sin x}-\frac{\cos x}{1+\sin x}=2 	an x $$

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Verify the identity by following steps:
- step0: Verify:
  $$\frac{\cos\left(xight)}{\left(1-\sin\left(xight)ight)}-\frac{\cos\left(xight)}{\left(1+\sin\left(xight)ight)}=2	an\left(xight)$$
- step1: Choose a side to work on:
  $$2	an\left(xight)=2	an\left(xight)$$
- step2: Verify the identity:
  $$	extrm{true}$$
Determine whether the expression $$ \sin(x) * 	an(x) + \cos(x) = 1/\cos(x) $$ is always true.
Verify the identity by following steps:
- step0: Verify:
  $$\sin\left(xight)	an\left(xight)+\cos\left(xight)=\frac{1}{\cos\left(xight)}$$
- step1: Choose a side to work on:
  $$\frac{1}{\cos\left(xight)}=\frac{1}{\cos\left(xight)}$$
- step2: Verify the identity:
  $$	extrm{true}$$
Both statements have been proven to be true:

a) $$ \sin x \cdot 	an x + \cos x = \frac{1}{\cos x} $$ is true.

b) $$ \frac{\cos x}{1 - \sin x} - \frac{\cos x}{1 + \sin x} = 2 	an x $$ is also true.
Both equations are proven to be true.

Prove that:
a)
b)

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Prove that: a) b)