secx - sinxcotx
= 1/cosx - sinx(1/tanx) color(red)(Note tanx = sinx/ cos x)
=1/cos x - sin x (cos x/sin x)
=1/cos x - cos x
=1/cos x - cos^2 x / cos x
= (1-cos^2 x) / cos x
=sin^2 x / cos x (Trig Identities - color(red)(cos^2x + sin^2 x =1)
=tanxsinx Note (color(red)(sinx/cosx=tanx)