err.. tan (3h)/h? simply plugging in 0 for x.. edit: are you sure x is approaching 0? initially, I thought it's h.. then the answer would have been 3+3tan(3x)^2 and you had to do some mess with identites.. http://www.clarku.edu/~djoyce/trig/identities.html
Look up a formula for tan(A+B) and apply it to tan(3x+3h). Then simplify, take your limit and use some trig.
It is actually very simple.. don't even need to any trig after simplifying tan(3x+3h) .. should factor out things.. and they would cancel out nicely. And, one more thing tan(x)/x = 1 .. (which is simple to prove is you know sin(x)/x =1 as x-->0)
Yep. You don't have to use any trig. But using sec^2(A)=1+tan^2(A) would put it in the simpler form listed in books.