SOLUTION: Please help I've tried to do it, but I don't know if I'm doing it right. Simplify the expression using one term, sin(alpha-beta)cos beta+cos(alpha-beta)sinbeta

Question 379130: Please help I've tried to do it, but I don't know if I'm doing it right.
Simplify the expression using one term, sin(alpha-beta)cos beta+cos(alpha-beta)sinbeta
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To answer the question you need to know the key Trig identities and how to recognize the patterns described by these identities. Knowing the identities is a matter of memorization. Recognizing patterns is a skill that takes practice.

For this expression, the pattern is:
sin(something)*cos(something-else) + cos(something)*sin(something-else)
And the identity that fits this patters is the right side of:
sin(A+B) = sin(A)cos(B) + cos(A)*sin(B)
Any expression that fits the pattern of the right side of this identity can be rewritten in the pattern of the left side. (It also works in the other direction, too. Any expression that fits the pattern of the left side can be rewritten in the pattern of the right side.)

Your expression fits the pattern of the right side with in the place of A and in the place of B. So we can rewrite it in the pattern of the left side with in the place of A and in the place of B:

which simplifies to:

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