Reciprocal Identities
$$\sin{x}$$
$$\frac{1}{\csc{x}}$$
$$\cos{x}$$
$$\frac{1}{\sec{x}}$$
$$\tan{x}$$
$$\frac{1}{\cot{x}}$$
$$\csc{x}$$
$$\frac{1}{\sin{x}}$$
$$\sec{x}$$
$$\frac{1}{\cos{x}}$$
$$\cot{x}$$
$$\frac{1}{\tan{x}}$$
Quotient Identities
$$\tan{x}$$
$$\frac{\sin{x}}{\cos{x}}$$
$$\cot{x}$$
$$\frac{\cos{x}}{\sin{x}}$$
Pythagorean Identities
$$\sin^2{x}+\cos^2{x}$$
$$1$$
$$\tan^2{x}+1$$
$$\sec^2{x}$$
$$1+\cot^2{x}$$
$$\csc^2{x}$$
Sum and Difference Identities
$$\sin{(\alpha+\beta)}$$
$$\sin{\alpha}\cos{\beta}+\cos{\alpha}\sin{\beta}$$
$$\sin{(\alpha-\beta)}$$
$$\sin{\alpha}\cos{\beta}-\cos{\alpha}\sin{\beta}$$
$$\cos{(\alpha+\beta)}$$
$$\cos{\alpha}\cos{\beta}-\sin{\alpha}\sin{\beta}$$
$$\cos{(\alpha-\beta)}$$
$$\cos{\alpha}\cos{\beta}+\sin{\alpha}\sin{\beta}$$
Double Angle Identities
$$\sin{2x}$$
$$2\sin{x}\cos{x}$$
$$\cos{2x}$$
$$\cos^2{x}-\sin^2{x}$$
$$2\cos^2{x}-1$$
$$1-2\sin^2{x}$$
Complementary Identities
$$\sin{\left(\frac{\pi}{2}-x\right)}$$
$$\cos{x}$$
$$\cos{\left(\frac{\pi}{2}-x\right)}$$
$$\sin{x}$$
Even/Odd Identities
$$\cos{(-x)}$$
$$\cos{(x)}$$
$$\sin{(-x)}$$
$$-\sin{x}$$