Trigonometric identities are fundamental equations that establish relationships between various trigonometric functions. Sin(θ/2) = ± √, Cos(θ/2) = ± √, Tan(θ/2) = ± √: These identities are helpful when dealing with half angles.Sin(θ ± φ) = Sinθ * Cosφ ± Cosθ * Sinφ, Cos(θ ± φ) = Cosθ * Cosφ ∓ Sinθ * Sinφ: These identities allow us to express the sine and cosine of the sum or difference of two angles.Sin(2θ) = 2 * Sinθ * Cosθ, Cos(2θ) = Cos²θ – Sin²θ, Tan(2θ) = 2 * Tanθ / (1 – Tan²θ): These identities are useful for simplifying expressions with double angles.Sin(π/2 – θ) = Cosθ, Cos(π/2 – θ) = Sinθ, Tan(π/2 – θ) = Cotθ: These identities define the relationships between trigonometric functions and their complementary angles.Tanθ = Sinθ / Cosθ and Cotθ = Cosθ / Sinθ: These identities relate tangent and cotangent to sine and cosine functions, respectively.Cscθ = 1 / Sinθ, Secθ = 1 / Cosθ, and Cotθ = 1 / Tanθ: These identities express cosecant, secant, and cotangent functions in terms of their reciprocal trig functions.1 + Tan²θ = Sec²θ and 1 + Cot²θ = Csc²θ: These identities relate the tangent and cotangent functions with secant and cosecant functions, respectively.Sin²θ + Cos²θ = 1: This identity is derived from the Pythagorean theorem and connects the sine and cosine functions.
