How can you prove \cot A = \frac{\cos A}{\sin 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}
\cot A=\frac{adj}{opp}=\frac{AB}{BC}
Step 3: "Prove the required equation.
PROVE: \cot A = \frac{\cos A}{\sin A}
L.H.S \cot = \frac{adj}{opp} ..................(1)
R.H.S \frac{\cos A}{\sin A} = \frac{\frac{adj}{hyp}}{\frac{opp}{hyp}}
= \frac{adj}{hyp} *\frac{hyp}{opp}
\frac{\cos A}{\sin A} = \frac{adj}{opp} ............................(2)
From equation (1) & (2)
we can conclude that L.H.S = R.H.S
So, \cot A = \frac{\cos A}{\sin A}
Hence proved.