Let f be the function defined by f(x) = (x+sinx)/cosx for -pi/2 < x < pi/2

1. state whether f is an even function or an odd function
2. find f'(x)
3. write an equation of the line tangent to the graph of f at the point where x=0

can someone please explain how to do this?!!! thank you!

1. f(-x) = (-x + sin(-x))/cos(-x) = -(x + sin(x))/cos(x) = - f(x)

So f is odd.

2. f '(x) = (cos(x)(1 + cos(x)) + sin(x)(x + sin(x)))/cos²(x) = (cos(x) + xsin(x) + 1)/cos²(x).

3. f '(0) = (1 + 0 + 1)/1 = 2 and f(0) = 0.

y = 2x.