Double angle formulae (HSC SSCE Mathematics Extension 1): Flashcards

sin 2θ = 2 sin θ cos θ

cos 2θ = cos²θ - sin²θ

tan 2θ = 2tan θ / (1 - tan²θ)

sin(θ + θ) = 2 sin θ cos θ

cos(θ + θ) = cos²θ - sin²θ

Set 2x = cos⁻¹(0.5) + 2nπ or 2x = -cos⁻¹(0.5) + 2nπ

x = 15° + n90° or x = 75° + n90°, n ∈ Z

tan(2x) = 2tan x / (1 - tan²x)

They simplify calculations and prove identities.

For simplification, solving equations, and proving identities.