Step-by-step explanation:
[tex] { \cot^{2}x}(1 + \tan^{2}x) \\ = \frac{1}{ \tan^{2}x} (1 + \tan^{2}x)[/tex]
[tex] = \frac{1}{ \tan^{2}x } + 1[/tex]
[tex] = \frac{ \cos^{2} x }{ \sin^{2}x } + 1 = \frac{ \cos^{2}x + \sin^{2}x}{ \sin^{2} x } [/tex]
[tex] = \frac{1}{ \sin^{2}x } = \csc^{2} x[/tex]
