[tex] \cos x \cot x + \sin x \\ = \cos x \times \frac{ \cos x }{ \sin x } + \sin x \\ = \frac{ \cos ^{2} x + \sin ^{2} x}{ \sin x } \\ = \frac{1}{ \sin x } \\ = cosec x \\ \purple { \boxed{ \bold{ \therefore \cos x \cot x + \sin x = \cosec x }}}[/tex]
