1. Finding the derivatives

this is a calc ab problem
f(x) = (x+sinx)/(cosx) for -π/2 < x <π/2
a)State whether this is an even or odd function
i thought it was odd because i graph it and also f(-x)=-f(x)
b)find f'(x)
((cosx)(1+cosx) - (x+sinx)*(-sinx))/((cosx)^2)
is there a more simplified way?
c) Write an equation of the line tangent to the graph of f at the point where x=0
Would I just subsitute 0 into the derivative formula and then put it into y=mx+b equation?