For \(\alpha\), \(\beta\), \(\alpha\pm\beta\) between \(0^\circ\) and \(90^\circ\):

$$\begin{align}

\sin(\alpha \pm \beta ) &= \sin\alpha \cos\beta \pm \cos\alpha \sin\beta \\[4pt]

\cos(\alpha \pm \beta ) &= \cos\alpha \cos\beta \mp \sin\alpha \sin\beta\end{align}$$

\sin(\alpha \pm \beta ) &= \sin\alpha \cos\beta \pm \cos\alpha \sin\beta \\[4pt]

\cos(\alpha \pm \beta ) &= \cos\alpha \cos\beta \mp \sin\alpha \sin\beta\end{align}$$

Adapting the trigonographs for angles outside the given range

makes for a nice exercise.

**Fun Fact:** Wikipedia’s “List of Trigonometric Identities” entry

features the trigonograph on the left. (I’m famous-ish!)