We need to complete the following identity:
[tex]\text{ \_\_\_\_}*\cos b=\frac{1}{2}[\sin(a+b)+\sin(a-b)][/tex]
For solving this problem, we need to check some known trigonometric identities, in this case we can use the following product identity:
[tex]\sin\alpha\cos\beta=\frac{\sin(\alpha+\beta)+\sin(\alpha-\beta)}{2}[/tex]
If we replace alpha by a and beta by b, we obtain:
[tex]\begin{gathered} \sin a*\cos b=\frac{\sin(a+b)+\sin(a-b)}{2} \\ \\ \text{ And this is equal to:} \\ \sin a\cos b=\frac{1}{2}[\sin(a+b)+\sin(a-b)] \end{gathered}[/tex]
The answer is C. sin a.
