Question

sin θ − csc θ cos θ

Answer 1

\[\sin \theta - \csc \theta \cos \theta = \frac{ \sin \theta }{ 1 } - \left( \frac{ 1 }{ \sin \theta } \cos \theta \right) = \frac{ \sin \theta }{ 1 } - \frac{ \cos \theta }{ \sin \theta } = \frac{ \sin^{2} \theta - \cos \theta }{ \sin \theta }\]

Answer 2

\[= \frac{ \sin^{2} - \cos \theta }{ \sin \theta } = \frac{ (1- \cos^{2} \theta) - \cos \theta }{ \sin \theta } = - \frac{ \cos^{2} \theta + \cos \theta - 1 }{ \sin \theta } \]