Gợi ý làm bài
a)
\(A = \tan ({90^0} - {72^0})\tan ({360^0} - {72^0}) + \sin {32^0}\sin ({180^0} - {32^0}) - \sin ({360^0} - {58^0})\sin ({180^0} - {58^0})\)
\(\eqalign{
& \cot {72^0}( - \tan {72^0}) + {\sin ^2}{32^0} + {\sin ^2}{58^0} \cr
& = - 1 + {\sin ^2}{32^0} + c{\rm{o}}{{\rm{s}}^2}{32^0} \cr
& = - 1 + 1 = 0 \cr} \)
b)
\(\eqalign{
& B = {{1 + ({{\sin }^2}\alpha + c{\rm{o}}{{\rm{s}}^2}\alpha )(si{n^2}\alpha - c{\rm{o}}{{\rm{s}}^2}\alpha )} \over {1 - ({{\sin }^2}\alpha + c{\rm{o}}{{\rm{s}}^2}\alpha )({{\sin }^4}\alpha - {{\sin }^2}\alpha c{\rm{o}}{{\rm{s}}^2}\alpha + c{\rm{o}}{{\rm{s}}^4}\alpha )}} \cr
& = {{1 + {{\sin }^2}\alpha - c{\rm{o}}{{\rm{s}}^2}\alpha } \over {1 - {\rm{[}}{{({{\sin }^2}\alpha + c{\rm{o}}{{\rm{s}}^2}\alpha )}^2} - 3{{\sin }^2}\alpha c{\rm{o}}{{\rm{s}}^2}\alpha }} \cr
& = {{3{{\sin }^2}\alpha } \over {3{{\sin }^2}\alpha c{\rm{o}}{{\rm{s}}^2}\alpha }} = {2 \over 3}(1 + {\tan ^2}\alpha ) \cr} \)
