I'm not sure how to get the final answer for this question I get stuck halfway thru.
Simplify using sum and difference identities:
cos((3pi/2)-x)
I think the answer is supposed to be
-sin(x)
Thanks!
Never mind I figured it out!
To simplify the expression cos((3π/2) - x) using the sum and difference identities, you need to know the identities:
1. cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
2. sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
In this case, we have cos((3π/2) - x). We can rewrite this as (3π/2) - x = 3π/2 - x.
Now, let's apply the sum and difference identity for cosine:
cos((3π/2) - x) = cos(3π/2)cos(x) + sin(3π/2)sin(x)
Since cos(3π/2) = 0 and sin(3π/2) = -1, we can substitute these values into the equation:
cos((3π/2) - x) = 0 * cos(x) - 1 * sin(x) = -sin(x)
So, the simplified expression is -sin(x).
If you were stuck halfway through, make sure you applied the sum and difference identity correctly and substituted the values of cos(3π/2) and sin(3π/2) accurately.