[tex] \\ sin^2 \alpha +cos^2 \alpha =1 ~~~~~~~~~cos^2x=1-sin^2x\\ csc \alpha = \frac{1}{sin \alpha } \\ cot \alpha = \frac{cos \alpha }{sin \alpha } \\ \\ \\ \frac{csc(x) - sin(x) }{cot(x)} = \\ = \frac{ \frac{1}{sin(x)} - sin(x) }{\frac{cos \alpha }{sin \alpha } } \\\ = \frac{ sin(x)(\frac{1}{sin(x)} - sin(x)) }{\frac{sinxcos \alpha }{sin \alpha } } \\ = \frac{1-sin^2(x)}{cos(x)} \\ = \frac{cos^2(x)}{cos(x)} \\ =\frac{cosx)cos(x)}{cos(x)} \\ =cos(x)[/tex]
