Verify that \(\frac{\sin \ A}{\sec \ A + \tan \ A - 1} + \frac{\cos \ A}{\text{cosec}\: A + \cot \ A - 1} = 1\)
Proof:
LHS \(= \frac{\sin \ A}{\sec \ A + \tan \ A - 1} + \frac{\cos \ A}{\text{cosec}\: A + \cot \ A - 1}\)
\(= \)
\(=\)
\(=\)
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\(=\)
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\(= \)
\(=\)
\(= \)
\(= \)
\(= \frac{2 \sin \ A \cos \ A}{2 \sin \ A \cos \ A}\)
\(= 1 = \) RHS
Hence, we proved.
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