\(\sin^2 21^\circ + \cos^2 89^\circ\)
\(= \sin^2 21^\circ + \cos^2 (90^\circ - 1^\circ)\)
\(= \sin^2 21^\circ + \sin^2 21^\circ\)
\(= 2\sin^2 21^\circ \ne 1\)
\(\sin^2 21^\circ + \cos^2 89^\circ\)
\(= \sin^2 21^\circ + \cos^2 (90^\circ - 1^\circ)\)
\(= \sin^2 21^\circ + \sin^2 21^\circ\)
\(= 2\sin^2 21^\circ \ne 1\)