If \(7 \ cot \ A = 24\), prove that \(\frac{1 - tan^2 \ A}{1 + tan^2 \ A} = cos^2 \ A - sin^2 \ A\).
Proof:
Given \(7 \ cot \ A = 24\)
\(cot \ A=\)
Let us consider the right-angled triangle \(ABC\).
If \(AB = 24k\) and \(BC = 7k\), where \(k\) is a positive number.
Then, \(AC=\)
\(sin \ A =\)
\(cos \ A =\)
\(tan \ A =\)
Consider LHS.
\(\frac{1 - tan^2 \ A}{1 + tan^2 \ A} =\)
Now, let us consider RHS.
\(cos^2 \ A - sin^2 \ A\)\(=\)
Therefore, LHS \(=\) RHS.
Hence, we proved.