To solve for the given expressions, we evaluate the following trigonometric values:
1. Sum of \(\sin 75^\circ\) and \(\sin 15^\circ\)
[tex]\[
\sin 75^\circ + \sin 15^\circ
\][/tex]
This expression needs to be checked if it equals to \(0.71\).
2. Difference between \(\sin 75^\circ\) and \(\sin 15^\circ\)
[tex]\[
\sin 75^\circ - \sin 15^\circ
\][/tex]
This expression needs to be checked if it equals to \(0.35\).
Now, let's interpret the results.
### Evaluation Results
- \(\sin 75^\circ + \sin 15^\circ\) is not equal to \(0.71\)
- \(\sin 75^\circ - \sin 15^\circ\) is not equal to \(0.35\)
Therefore, none of the given expressions are correct in equating to the provided values. Given this, the correct selections should be reflecting that neither equation holds true for the given values:
- \(\sin 75^\circ + \sin 15^\circ = 0.71\) \( \rightarrow \) False
- \(\sin 75^\circ - \sin 15^\circ = 0.35\) \( \rightarrow \) False
So, select False from both drop-down menus.
