Trig Identities

The trigonometric identities are mathematical equations that relate the trigonometric functions (sin, cos, tan) to one another.
There are many identities in trigonometry, but for revision, we are focusing on the primary ones: Pythagorean identities, Quotient identities, Co-Function identities, and Even-Odd identities.
Pythagorean identities form the basis of trigonometry and are based on the Pythagorean theorem. These include sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, and cot²θ + 1 = csc²θ.
Quotient identities express the functions in terms of each other. tan(θ) = sin(θ)/cos(θ) and cot(θ) = cos(θ)/sin(θ).
Co-Function identities describe the relationship between the sine and cosine of complementary angles. sin(90° – θ) = cos(θ) and cos(90° – θ) = sin(θ)
Even-Odd identities pertain to the symmetry of the sin, cos, and tan functions. sin(–θ) = -sin(θ), cos(–θ) = cos(θ), and tan(–θ) = -tan(θ).
The key to mastering trig identities is practise. Work through several examples and apply each identity correctly.
Remember, these identities will help later when solving trig equations or simplifying expressions.