If \(\sin(A + B) = 1\) and \(\cos(A - B) = 1\), then find the value of \(\cot 2A\), given that \(0^\circ \leq (A + B) \leq 90^\circ\) and \(A \geq B\).

Q.If \(\sin(A + B) = 1\) and \(\cos(A - B) = 1\), then find the value of \(\cot 2A\), given that \(0^\circ \leq (A + B) \leq 90^\circ\) and \(A \geq B\).

\(\sin(A + B) = 1 = \cos(A - B)\) Or, \(\sin(A + B) = \sin [90^\circ - (A - B)]\) ⇒ \(A + B = 90^\circ - (A - B)\) ⇒ \(A + B + A - B = 90^\circ\) ⇒ \(2A = 90^\circ\)

\(\therefore \cot 2A = \cot 90^\circ = 0\)