These formulas express the sine, cosine, tangent, and cotangent of the sum or difference of two angles \(\alpha\) and \(\beta\). They are fundamental in trigonometry for simplifying expressions involving angle sums.
\[ \sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \]
Explanation: The sine of the sum or difference of two angles is expressed as a combination of products of sines and cosines of the individual angles.
\[ \cos(\alpha \pm \beta) = \cos \alpha \cos \beta \mp \sin \alpha \sin \beta \]
Explanation: The cosine of the sum or difference is given by the difference or sum of products of cosines and sines, respectively.
\[ \tan(\alpha \pm \beta) = \frac{\tan \alpha \pm \tan \beta}{1 \mp \tan \alpha \tan \beta} \]
Explanation: Tangent of sum or difference converts to a rational expression involving the tangents of the individual angles.
\[ \cot(\alpha \pm \beta) = \frac{\cot \alpha \cot \beta \mp 1}{\cot \beta \pm \cot \alpha} \]
Explanation: Cotangent of the sum or difference is represented as a rational function of cotangents of the angles.