(Tan/cot)- (sec/cos)

you need an angle or argument behind the trig operators, otherwise it is like saying

log + √

e.g. tanx/cotx - secx/cosx
= (sinx/cosx)/(cosx/sinx) - (1/cosx)/(cosx
= sin^2 x/cos^2 x - 1/cos^2 x
= (sin^2 x - 1)/cos^2 x
= -cos^2 x/cos^2 x
= -1