Trigonometry

Reciprocal Identities

\[ \tan A = \frac{\sin A}{\cos A} \]

\[ \sec A = \frac{1}{\cos A} \]

\[ \csc A = \frac{1}{\sin A} \]

\[ \sin^2 A + \cos^2 A = 1 \]

\[ \sec^2 A = 1 + \tan^2 A \]

\[ \csc^2 A = 1 + \cot^2 A \]

\[ \sin(A \pm B) = \sin A \cos B \pm \cos A \sin B \]

\[ \cos(A \pm B) = \cos A \cos B \mp \sin A \sin B \]

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

\[ \sin 2A = 2 \sin A \cos A \]

\[ \cos 2A = \cos^2 A - \sin^2 A = 2 \cos^2 A - 1 = 1 - 2 \sin^2 A \]