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The value of \(1 + \cot^2 A\) is:

  • A.\(\sec^2 a\)
  • B.\(\csc^2 a\)
  • C.\(\sin^2 a\)
  • D.\(\cos^2 a\)

Answer: B

This is a fundamental Pythagorean identity, derived by dividing \(\sin^2 A + \cos^2 A = 1\) by \(\sin^2 A\).

\(\frac{\sin^2 A}{\sin^2 A} + \frac{\cos^2 A}{\sin^2 A} = \frac{1}{\sin^2 A}\)

\(1 + \cot^2 A = \csc^2 A\).

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