Recall the following sum-to-product formulas of trigonometric function
[tex]\sin \alpha+\sin \beta=2\sin \mleft(\dfrac{\alpha+\beta}{2}\mright)\cos \mleft(\dfrac{\alpha−\beta}{2}\mright)[/tex]Given the sum
[tex]\begin{gathered} \sin 3\degree+\sin 37\degree \\ \\ \alpha=3\degree \\ \beta=37\degree \end{gathered}[/tex]Then the product is
[tex]\begin{gathered} \sin 3\degree+\sin 37\degree=2\sin \mleft(\dfrac{3\degree+37\degree}{2}\mright)\cos \mleft(\dfrac{3\degree-37\degree}{2}\mright) \\ \\ \text{Simplifying we get} \\ \sin 3\degree+\sin 37\degree=2\sin \Big{(}\dfrac{40\degree}{2}\Big{)}\cos \Big(\dfrac{-34\degree}{2}\Big) \\ \sin 3\degree+\sin 37\degree=2\sin (20\degree)\cos (-17\degree) \end{gathered}[/tex]