[tex]cot(x- \frac{ \pi }{2} )= \frac{1}{tan(x- \frac{ \pi }{2} )} [/tex]
[tex]tan(x- \frac{ \pi }{2} )= \frac{sin(x- \frac{ \pi }{2} )}{cos(x- \frac{ \pi }{2} )}= [/tex]
[tex] \frac{sinx*cos( \frac{ \pi }{2})-cosx*sin( \frac{ \pi }{2})}{cosx*cos( \frac{ \pi }{2})+sinx*sin( \frac{ \pi }{2})} = \frac{-cosx}{sinx}=-cotx=-1/tanx [/tex]
(cos π/2 = 0, sin π/2 = 1)
so
[tex]cot(x- \frac{ \pi }{2} )= \frac{1}{tan(x- \frac{ \pi }{2} )}= \frac{1}{-1/tanx}=-tanx [/tex]
