Verify that \(sin^2 A \ cos^2 B + cos^2 A \ sin^2 B + cos^2 A \ cos^2 B + sin^2 A \ sin^2 B = 1\)
Proof:
Consider the LHS \(sin^2 A \ cos^2 B + cos^2 A \ sin^2 B + cos^2 A \ cos^2 B + sin^2 A \ sin^2 B = 1\)
\(= sin^2 A(cos^2 B + sin^2 B) + cos^2 A (sin^2 B + cos^2 B)\)
\(= sin^2 A (\)\()\) \(+\) \(cos^2 A\) \((\)\()\)
\(= sin^2 A + cos^2 A\)
\(=\) [By the identity ]
Hence, proved.