Explanation
The product-to-sum formula can be seen below.
[tex]cosAsinB=\frac{1}{2}(sin(A+B)-sin(A-B))[/tex]
Therefore, we can insert the values of the angles into the formula
[tex]\begin{gathered} Cos37.5sin7.5=\frac{1}{2}(sin(37.5+7.5)-sin(37.5-7.5)) \\ =\frac{1}{2}(sin45-sin30) \\ =\frac{1}{2}(\frac{\sqrt{2}}{2}-\frac{1}{2}) \\ =(\frac{\sqrt{2}}{4}-\frac{1}{4}) \\ =\frac{\sqrt{2}-1}{4} \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} A=2 \\ B=1 \end{gathered}[/tex]
