Trigonometry - Further Identities (Edexcel A-Level Mathematics): Flashcards

They find sine, cosine, or tangent of angle sums or differences.

$\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B$

$\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B$

$\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$

$\sin(2\theta) = 2 \sin \theta \cos \theta$

$\cos(2\theta) = \cos^2 \theta - \sin^2 \theta$

$\tan(2\theta) = \frac{2\tan \theta}{1 - \tan^2 \theta}$

$\sin(\frac{\theta}{2}) = \pm \sqrt{\frac{1 - \cos \theta}{2}}$

$\cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos \theta}{2}}$

They convert products of sine and cosine into sums.