# 16.4: Trigonometric Identities

• $$\sin^2 u + \cos^2 u = 1$$
• $$\tan u = \frac{\sin u}{\cos u}$$
• $$\sin \left( \frac{\pi}{2} − u \right) = \cos u$$
• $$\cos \left( \frac{\pi}{2} − u \right) = \sin u$$
• $$\sin (u \pm v) = \sin u \cos v \pm \cos u \sin v$$
• $$\cos (u \pm v) = \cos u \cos v \mp \sin u \sin v$$
• $$\sin (−u) = − \sin u$$
• $$\cos (−u) = \cos u$$
• $$\tan (−u) = − \tan u$$
• $$\sin u \cos v = \frac{1}{2} \left[ \sin (u + v) + \sin (u − v) \right]$$
• $$\sin u \sin v = \frac{1}{2} \left[ \cos (u − v) − \cos (u + v) \right]$$
• $$\cos u \cos v = \frac{1}{2} \left[ \cos (u − v) + \cos (u + v) \right]$$