Is \frac{sin A}{cos A} equal to \tan A?

Step 1: Make a right angle triangle
NOTE: ABC is a right angle triangle, right angle at B
Step 2: Recall the trigonometric ratios formulas
\sin A = \frac{opp}{hyp} = \frac{CB}{AC}
\cos A = \frac{adj}{hyp} = \frac{AB}{AC}
\tan A = \frac{opp}{adj} = \frac{CB}{AC}
Step 3: Prove the required equation.
PROVE: \tan A = \frac{\sin A}{\cos A}
L.H.S \tan = \frac{opp}{adj} ..................(1)
R.H.S \frac{\sin A}{\cos A} = \frac{\frac{opp}{hyp}}{\frac{adj}{hyp}}
= \frac{opp}{hyp} *\frac{hyp}{adj}
\frac{\sin A}{\cos A} = \frac{opp}{adj} ............................(2)
From equation (1) & (2)
we can conclude that L.H.S = R.H.S
So, \tan A = \frac{\sin A}{\cos A}
Hence proved.