Trigonometry Sheet 4

Compound Angle Formulas (Sum & Difference)

1. Sine & Cosine Sum/Difference

Function Formula Result
$$\sin(A + B)$$ $$\sin A \cos B + \cos A \sin B$$
$$\sin(A – B)$$ $$\sin A \cos B – \cos A \sin B$$
$$\cos(A + B)$$ $$\cos A \cos B – \sin A \sin B$$
$$\cos(A – B)$$ $$\cos A \cos B + \sin A \sin B$$

2. Tangent & Cotangent Sum/Difference

Function Formula Result
$$\tan(A + B)$$ $$\frac{\tan A + \tan B}{1 – \tan A \tan B}$$
$$\tan(A – B)$$ $$\frac{\tan A – \tan B}{1 + \tan A \tan B}$$
$$\cot(A + B)$$ $$\frac{\cot A \cot B – 1}{\cot B + \cot A}$$
$$\cot(A – B)$$ $$\frac{\cot A \cot B + 1}{\cot B – \cot A}$$
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