in the interval [x,x+h]

f(x)=tan(x)

Avg. rate of change = (f(x+h)-f(x))/(x+h-x)\

= (tan(x+h) - tan(x))/h

I need this to equal (tanh/h)*((sec^2(x))/(1-tanxtanh))

I'm thinking tan addition forumula...

[((tanx+tanh)/(1-tanxtanh)) -tanx]/h

I tried common denominator on the top, factoring out a tanh, but I'm going in circles. Please help.