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?

thanks in advance