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

1. B f(x)=4sinx/2-3

2. B, F, G (c=-1. a=2, b=2)

3. c. H(t)=-2.4cos(0.017t)+12

4. A, B, E, F (y=cos^-1x, y=cot^-1x, y=sin^-1x, y=tan^-1x)

5. C y=sin^-1x

6. C 48.7

7. C f(g(x))=sec(sinx) domain: all real #

8. C step 3

Explanation:

Answer 2

we have that

Step 1: f(x)=sinA, where A=arctan x and x = tanA-----> is correct
Step 2: tanA= opp/adj=x/1-----------> is correct
Step 3: hypotenuse= square root of 1²-x²= square root of 1-x²-----> is not correct
Because hypotenuse= square root of (1² + x²)=square root of (1+x²)
Step 4: sinA=opp/hyp=x/square root of (1+x²)

the answer is
In step 3 Martin make is first error