a)
\(\eqalign{
& {\tan ^2}\alpha + {\cot ^2}\alpha \cr
& = {(\tan \alpha + \cot \alpha )^2} - 2\tan \alpha \cot \alpha = {m^2} - 2 \cr} \)
b)
\(\eqalign{
& {\tan ^3}\alpha + {\cot ^3}\alpha \cr
& = (\tan \alpha + \cot \alpha )({\tan ^2}\alpha - \tan \alpha \cot \alpha + {\cot ^2}\alpha ) \cr
& = m({m^2} - 3) \cr} \)
