Mệnh đề nào sau đây là sai?

\(\tan \alpha .\cot \alpha = 1\left( {\alpha \ne k\frac{\pi }{2},k \in Z} \right)\).

\(\tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }}\left( {\alpha \ne \frac{\pi }{2} + k\pi ,k \in Z} \right)\).

\({\sin ^2}\alpha - {\cos ^2}\alpha = 1\).

\(1 + {\cot ^2}\alpha = \frac{1}{{{{\sin }^2}\alpha }}\left( {\alpha \ne k\pi ,k \in Z} \right)\).