Trig Identities

In this lesson we learn:
- Trig identities: The tools for simplifying trig expressions
- Addition identities: Simplify trig functions of sums
- Negative angle identities: Simplify trig functions of negative angles
- Subtraction identities: Simplify trig functions of differences
- Double angle identities: Trig functions of twice an angle
- Triple angle identities: Trig functions of three times an angle
- Pythagorean identities: Relating squares of trig functions
- Half angle identities: Trig functions of half an angle

sin(2a) = sin(a+a) = sin(a) cos(a) + cos(a) sin (a) = 2 sin(a) cos(a)

sin (A+B) = sin A cos B + cos A sin B
cos (A+B) = cos A cos B − sin A sin B
tan (A+B) = (tan A + tan B) / (1 − tan A tan B)
sin (A−B) = sin A cos B − cos A sin B
cos (A−B) = cos A cos B + sin A sin B
tan (A−B) = (tan A − tan B) / (1 + tan A tan B)

Sin 2A = 2 sin A cos A
cos 2A = cos^2 A – sin^2 A
tan 2A = (2 tan A) / (1 – tan^2 A)

sin 3A = 3sin A cos^2 A - sin^3 A
cos 3A = cos^3 A - 3sin^2 A cos A
tan 3A = (3tan A - tan^3 A) / (1 - 3tan^2 A)
Sin^2 + cos^2 = 1
1 + tan^2 = sec^2
Cot^2 + 1 = csc^2
Sin^2 A/2 = (1 − cos A) /  2
Cos^2 A/2 = (1 + cos A) / 2
Tan^2 A/2 = (1 − cos A) / (1 + cos A)

Trig identities - Addition identities - Negative angle identities: 

Subtraction identities - Double angle identities - Triple angle identities | Trig identities: 

Pythagorean identities - Half angle identities | Trig identities: