SIMPLIFYING TRIGONOMETRIC IDENTITIES AND EXPRESSIONS

TRIGONOMETRIC IDENTITIES such as the Reciprocal identities, quotient identities and pythogorean identities. Familiarizing these identities are primary prior knowledge to simplify, verify, or prove problems on trigonometric expressions or identities.

Reciprocal Identities:
a. sin (θ) = 1 / csc (θ) and csc (θ) = 1 / sin (θ)
b. cos (θ) = 1 / sec (θ) and sec (θ) = 1 / cos (θ)
c. tan (θ) = 1 / cot (θ) and cot (θ) = 1 / tan (θ)

Pythagorean Identities: Note: 2 in each identity is exponent.
a. sin^2θ + cos^2θ = 1 ⇒ 1 - sin^2θ = cos^2 θ ⇒ 1 - cos^2θ = sin^2θ
b. sec^2θ - tan^2θ = 1 ⇒ sec^2θ = 1 + tan^2θ ⇒ sec^2θ - 1 = tan^2θ
c. csc^2θ - cot^2θ = 1 ⇒ csc^2θ = 1 + cot^θ ⇒ csc^2θ - 1 = cot^2θ

Quotient Identities:
a. tan(θ)= sin(θ) /cos(θ)
​b. cot (θ)= cos(θ) /sin(θ)