High School Trigonometry/Fundamental Identities

Reciprocal Identities
$$\sin u=\left (\frac{1}{\csc u} \right)$$ $$\cos u=\left (\frac {1}{\sec u}\right)$$

$$\tan u=\left(\frac{1}{\ cot u} \right)$$ $$\csc u=\left(\frac{1}{\sin u}\right)$$

$$\sec u=\left(\frac{1}{\cos u}\right)$$ $$\cot u=\left(\frac{1}{\tan u}\right)$$

Pythagorean Identities
$$\sin^2 u + \cos^2 u=1$$

$$1+\tan^2 u=\sec^2$$

$$1+\cot^2 u=\csc^2 u$$

Quotient Identities
$$\tan u=\left(\frac{\sin u}{\cos u}\right)$$ $$\cot u=\left(\frac{\cos u}{\sin u}\right)$$

Co-Function Identities
$$\sin (\left(\frac{\pi}{2}\right) - u)= \cos u$$ $$\cos (\left(\frac{\pi}{2}\right) - u)=\sin u$$

$$\tan (\left(\frac{\pi}{2}\right)- u)=\cot u$$ $$\csc (\left(\frac{\pi}{2}\right)- u)=\sec u$$

$$\sec (\left(\frac{\pi}{2}\right)-u)=\csc u$$ $$\cot (\left(\frac{\pi}{2}\right)-u)=\tan u$$

Even-Odd Identities
$$\sin (-u)=-\sin (u)$$ $$\cos (-u)=cos (u)$$

$$\tan (-u)=-\tan (u)$$ $$\csc (-u)=-\csc (u)$$

$$\sec (-u)=\sec (u)$$ $$\cot (-u)=-\cot (u)$$