Eulers Method - proving a solution

First off, I read the sticky, I hope to understand it all one day (Giggle)

I am supposed to verify the the solution of the differential equation:

Solution: -cosx ln abs(secx + tan x). The equation is y" +y = tanx

Now, I have the solution spelled out in my answer guide, but I don't know how they got from step to step (just so you know I'm not looking for an answer handout)

You will need the second derivative of that lovely expression.

Substitute into the Differential equation.

After a little algebra, you should be able to demonstrate equality.

That's all there is to it.