LON-CAPA trig_id001.problem

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$\textrm{Which of the following statements is false?}$

$\textrm{For all } \alpha \textrm{ where } \tan \, \alpha \textrm{ is defined and nonzero,} \; \cos \, \alpha \, = \, \frac{\sin \, \alpha}{\tan \, \alpha} \, .$

$\textrm{For all } \alpha \textrm{ where } \cos \, \alpha \textrm{ is nonzero,} \; 1 \ + \ \tan^{\small{2}} \, \alpha \, = \, \sec^{\small{2}} \, \alpha \, .$

$\textrm{For all } \alpha \textrm{ where } \sin \, \alpha \textrm{ is nonzero,} \; \sin \, \alpha \, = \, \frac{1}{\csc \, \alpha} \, .$

$\textrm{For all } \alpha, \; \cos^{\small{2}} \, \alpha \, = \, {1\ +\ \sin^{\small{2}} \, \alpha} \, .$

$\textrm{For all } \alpha \textrm{ where both } \tan \, \alpha \textrm{ and } \cot \, \alpha \textrm{ are defined and nonzero,} \; \tan \, \alpha \, \cdot \, \cot \, \alpha \, = \, 1 \, .$

$\textrm{None of the above}$

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