Fast martin simplified the composed function f(x)=sin(arctan x). his work is shown below. step 1: f(x)=sina, where a=arctan x and x = tana step 2: tana= opp/adj=x/1 step 3: hypotenuse= square root of 1^2-x^2= square root of 1-x^2 step 4: sina=opp/hyp=x/squareroot 1-x^2 in which step did martin make is first error?

We will evaluate Martin's work step by step:
 Step 1: 
 f (x) = sinA,
 where
 A = arctan x
 and
 x = tanA
 step 1 it's OK
 Step 2: 
 tanA = opp / adj = x / 1
 step 2 it's OK
 Step 3: 
 hypotenuse = square root of 1 ^ 2-x ^ 2 = square root of 1-x ^ 2
 step 3 it's NOT OK
 The correct form in this case is:
 hypotenuse = square root of 1 ^ 2 + x ^ 2 = square root of 1 + x ^ 2
 
 Martin did make his first mistake in Step 3.

What exactly is your question?