algebra precalculus - Verify trigonometric equation $frac{(sec{A}-csc{A})}{(sec A+csc A)}=frac{(tan A-1)}{(tan A+1)}$

How Would I verify the following identity.

$$\frac{(\sec{A}-\csc{A})}{(\sec A+\csc A)}=\frac{(\tan A-1)}{(\tan A+1)}$$

I simplified it to

$$\frac{(\sin{A}-\cos{A})}{(\sin{A} \cos{A})}\div\frac{(\sin{A}+\cos{A})}{(\sin{A}\cos{A})}$$

Answer

Hint: Start by multiplying top and bottom on the left by $\sin A$.