Trigonometry/Identities/Table

Reciprocal

 * $$\csc\theta=\frac{1}{\sin\theta}$$


 * $$\sec\theta=\frac{1}{\cos\theta}$$


 * $$\cot\theta=\frac{1}{\tan\theta}$$

Quotient

 * $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$


 * $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$

Pythagorean

 * $$\tan^2\theta+1=\sec^2\theta$$


 * $$1+\cot^2\theta=\csc^2\theta$$


 * $$\sin^2\theta+\cos^2\theta=1$$

Negative-angle

 * $$\sin(-\theta)=-\sin\theta$$


 * $$\cos(-\theta)=\cos\theta$$


 * $$\tan(-\theta)=-\tan\theta$$

Sum and difference

 * $$\sin(A+B)=\sin A\cos B+\cos A \sin B$$


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


 * $$\tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$$


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


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


 * $$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$$

Cofunction

 * $$\cos(90^o-\theta)=\sin\theta$$


 * $$\sec(90^o-\theta)=\csc\theta$$


 * $$\cot(90^o-\theta)=\tan\theta$$


 * $$\sin(90^o-\theta)=\cos\theta$$


 * $$\csc(90^o-\theta)=\sec\theta$$


 * $$\tan(90^o-\theta)=\cot\theta$$

Double-angle

 * $$\cos2A=\cos^2A-\sin^2A$$


 * $$\cos2A=2\cos^2A-1$$


 * $$\cos2A=1-2\sin^2A$$


 * $$\sin2A=2\sin A\cos A$$


 * $$\tan2A=\frac{2\tan A}{1-\tan^2A}$$

Half-angle

 * $$\tan\frac{A}{2}=\pm \sqrt{\frac{1-\cos A}{1+\cos A}}$$


 * $$\tan\frac{A}{2}=\frac{\sin A}{1+\cos A}$$


 * $$\tan\frac{A}{2}=\frac{1-\cos A}{\sin A}$$


 * $$\cos\frac{A}{2}=\pm \sqrt{\frac{1+\cos A}{2}}$$


 * $$\sin\frac{A}{2}=\pm \sqrt{\frac{1-\cos A}{2}}$$