Okay the domain shoudl be straight forward

D={x is All Reals except when x = Pi/2 + K(Pi)} where K is an Odd Interger

A vertical Asymptote exists at Pi/2 + K(Pi) where K is an Odd Interger

F'(x)

just the addition rule, (tanx)' + (sinx)' = sec^2x + cosx

so simpleify to cos

you end up with 1+cos^3x/cos^2, I must be missing an identity to simplify this, any ideas?