Question

HELP FAST PLEASE!!

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?

Answer 1

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
Answer:
Martin did make his first mistake in Step 3.