Write the tangent as ratio of sine over cosine, and use the definition:
Note that:
and also:
The numerator becomes:
Put these in the common denominator to get:
I hope this is helpful.
"Use the limit definition of the derviative to prove the derivative for the function y = tan x is sec^2 x
(You'll need to use the lim as h goes to 0 (sin h/h) as well as the identity for the tangent of the sum of two angles)"
I know that that's the derivative, but I have no idea how to prove it. Please help!