Originally Posted by

**Kakariki** I am rather terrible at using trigonometric proofs, which is needed in doing this question.

Question is title of this thread.

My attempt:

$\displaystyle \frac{tan(x+h) - tanx}{h} $

$\displaystyle = \frac{\frac{sin(x+h)}{cos(x+h)} - \frac{sinx}{cosx}}{h} $

$\displaystyle = \frac{\frac {sinxcosh + cosxsina}{cosxcosh - sinxsinh} - \frac{sinx}{cosx}}{h} $

I don't know what to do from here. I need to show all my steps to get the answer. I know the answer is $\displaystyle sec^2 x $, but don't know how to show it using first principles.

If you could show me what to do next, I would be very grateful.