Answer
$d$
Work Step by Step
$\sin{(45+x)}+ \sin{(45-x)}=$
$$\sin{(45)} \cos{x} + \cos{(45)} \sin{x} + \sin{(45)} \cos{x} - \cos{(45)} \sin{x}$$
$\sin{(45+x)}+ \sin{(45-x)}= 2 \sin{(45)} \cos{x} = \sqrt{2} \cos{x}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.