To solve this problem, we will use the following identity:
[tex]\sin (a+b)=\sin a\cos b+\cos a\sin b\text{.}[/tex]
Using the above identity we can rewrite the given expression as follows:
[tex]\sin (35^{\circ}+115^{\circ}).[/tex]
Simplifying the above result, we get:
[tex]\sin (150^{\circ})\text{.}[/tex]
Answer:
[tex]\sin (150^{\circ})\text{.}[/tex]
