Step-by-step explanation:
[tex] \csc x \: \cos x = \frac{1 - { \sin}^{2}x }{ \sin x \: cos x} \\ \\ rhs = \frac{1 - { \sin}^{2}x }{ \sin x \: cos x} \\ \\ = \frac{ { \cos}^{2} x}{ \sin x \: cos x} \\ \\ = \frac{ { \cos} x}{ \sin x} \\ \\ = \frac{ { 1} }{ \sin x} \times \cos \\ \\ = \csc x \: \cos x \\ \\ = lhs \\ hence \: proved \\ [/tex]
