Here we want to see in which step does Bob make a mistake, we will see that it happens in step 1, where he expands incorrectly the sine of a sum
Sine of the sum expansion.
The sine of a sum can be written as:
sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
While if you look at step 1, he uses a negative sign instead of a positive one, what he should wrote is:
sin(3*pi/2 + x) = sin(3*pi/2)*cos(x) + cos(3*pi/2)*cos(x)
Now we know that:
- sin(3*pi/2) = -1
- cos(3*pi/2) = 0
Then:
sin(3*pi/2 + x) = -cos(x)
So Bob got correct the steps 2 and 3, but there is still a mistake in the first one.
If you want to learn more about trigonometry, you can read:
https://brainly.com/question/8120556
