Question

Review the steps of the proof of the identity

At which step was an error made?
sin (A-3) - COSA.
= A.
step 1
step 2
3п
sin
step 3
step 4
Step 1: = sinAcos
3 п
2
-
COSAsin
n ()
Step 2: = (sinA)(0) + COSA( - 1)
Step 3: = (sinA)(0) + (1) (COSA)
Step 4: = 0 + COSA
Step 5: Cos A

Answer 1

step 2

and then also in step 3 compensating the error in step 2

Explanation:

I think I just answered this for another post.

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

so, step 1 is correct :

sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2)

but step 2 suddenly and incorrectly switched that central "-" to a "+".

yes, sin(3pi/2) = -1, but that is still an explicit factor in step 2. so it was not used to flip the central operation from subtraction to addition, and therefore this change was a mistake.

then, in step 3, another error was made by just ignoring the "-" sign of "-1" and still keeping the central "+" operation. this error compensated for the error in step 2 bringing us back by pure chance to the right result.