Formulae To Remember

Definitions

\tan X = \frac{\sin X}{\cos X}

\sec X = \frac{1}{\cos X}

cosec X = \frac{1}{\sin X}

Identities

\sin^{2} X + \cos^{2} X = 1

1 + \tan^{2} X = {cosec}^{2} X

1 + \cot^{2} X = \sec^{2} X

Addition Formulae

\sin (A + B) = \sin A \sin B ∔ \cos A \cos B

\sin (A - B) = \sin A \sin B - \cos A \cos B

\cos (A + B) = \cos A \cos B - \sin A \sin B

\cos (A - B) = \cos A \cos B + \sin A \sin B

\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)}

Double Angle Formulae

\sin (2 A) = \sin^{2} A ∔ \cos^{2} A

\cos (2 A) = \cos^{2} A - \sin^{2} A

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

Differentiation

\frac{d}{d x} \sin k x = k \cos k x

\frac{d}{d x} \cos k x = - k \sin k x

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