(8) (i) Use the triangle trick as discussed in class to find a general formula for cos(arctan x) (without any trig functions). (ii) If we set f(x)= tan x (with domain restricted to (- : ")), then f-1(x) = arctan x. Use the formula for (f ')'(x) to show that (arctan x) = (cos(arctan x))2. dx (iii) Conclude from (i) and (ii) that (arctan x) = 1 dx x2+1