Mathematics

The key is recognizing that $75°$ isn't a standard angle, but it is a sum of two angles you know well: $45° + 30°$. Use the sine addition formula $\sin(A + B) = \sin A \cos B + \cos A \sin B$ to break it into pieces you can evaluate exactly. Once you substitute the known values for $\sin 45°$, $\cos 45°$, $\sin 30°$, and $\cos 30°$, you'll combine them into a single exact form.

The key is recognizing that $75°$ isn't a standard angle, but it is a sum of two angles you know well: $45° + 30°$. Use the sine addition formula $\sin(A + B) = \sin A \cos B + \cos A \sin B$ to break it into pieces you can evaluate exactly. Once you substitute the known values for $\sin 45°$, $\cos 45°$, $\sin 30°$, and $\cos 30°$, you'll combine them into a single exact form.