Sine, Cosine, and Tangent of Sum and Difference of Angles
Big Idea: Instead of measuring angles one at a time, we can break complex angles into sums or differences of simpler angles. These powerful formulas let us find exact values of trigonometric functions for angles like $75°$, $15°$, $105°$, and many more!
📐 The Sum and Difference Formulas
Sine Formulas
$$ \sin(A + B) = \sin A \cos B + \cos A \sin B $$
$$ \sin(A - B) = \sin A \cos B - \cos A \sin B $$
Cosine Formulas
$$ \cos(A + B) = \cos A \cos B - \sin A \sin B $$
$$ \cos(A - B) = \cos A \cos B + \sin A \sin B $$
Tangent Formulas
$$ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} $$
$$ \tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} $$