Title: Trig Identities

Q: Pythagorean Identity: Sine and Cosine
A: [$$]\sin^2(x) + \cos^2(x) = 1[/$$]

Q: Pythagorean Identity: Tangent and Secant
A: [$$]1 + \tan^2(x) = \sec^2(x)[/$$]

Q: Pythagorean Identity: Cotangent and Cosecant
A: [$$]1 + \cot^2(x) = \csc^2(x)[/$$]

Q: Even/Odd Properties of Sine and Cosine
A: [$$]\sin(-x) = -\sin(x), \quad \cos(-x) = \cos(x)[/$$]

Q: Periodicity of Sine and Cosine
A: [$$]\sin(x + 2 \pi) = \sin(x), \quad \cos(x + 2 \pi) = \cos(x)[/$$]

Q: Translation Relation Between of Sine and Cosine
A: [$$]\sin(x) = \cos(x - \pi/2)[/$$]

Q: Law of Sines
A: [$$]\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}[/$$]

Q: Law of Cosines
A: [$$]a^2 = b^2 + c^2 - 2bc \cos(A)[/$$]

Q: Addition Formula for Sine
A: [$$]\sin(x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)[/$$]

Q: Addition Formula for Cosine
A: [$$]\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)[/$$]

Q: Addition Formula for Tangent
A: [$$]\tan(x + y) = \frac{\tan(x) + \tan(y)}{1 - \tan(x) \tan(y)}[/$$]

Q: Double-Angle Formula for Sine
A: [$$]\sin(2x) = 2 \sin(x) \cos(x)[/$$]

Q: Double-Angle Formula for Cosine
A: [$$]\cos(2x) = \cos^2(x) - \sin^2(x)[/$$]

Q: Double-Angle Formula for Tangent
A: [$$]\tan(2x) = \frac{2 \tan(x)}{1 - \tan^2(x)}[/$$]

Q: Half-Angle Formula for Sine
A: [$$]\sin^2(x) = \frac{1 - \cos(2x)}{2}[/$$]

Q: Half-Angle Formula for Cosine
A: [$$]\cos^2(x) = \frac{1 + \cos(2x)}{2}[/$$]