[tex] \sin \alpha ( \csc \alpha - \sin \alpha )[/tex]
but
[tex] \csc\alpha = \frac{1}{ \sin \alpha } [/tex]
now substituting it in the formula
[tex] \sin \alpha ( \frac{1}{ \sin \alpha } - \sin \alpha )[/tex]
now multiplying with the sine alpha throughout the equation
[tex] = \frac{ \sin \alpha }{ \sin \alpha } - {sin}^{2} \alpha [/tex]
[tex] = 1 - {sin}^{2} \alpha [/tex]
but mathematically
[tex]1 - {sin}^{2} \alpha = {cos}^{2} \alpha [/tex]
hence proved.
