Sum and difference of two angles (HSC SSCE Mathematics Extension 1): Flashcards

sin(θ + φ) = sin θ cos φ + cos θ sin φ

cos(θ + φ) = cos θ cos φ - sin θ sin φ

tan(θ + φ) = (tan θ + tan φ) / (1 - tan θ tan φ)

sin(θ - φ) = sin θ cos φ - cos θ sin φ

cos(θ - φ) = cos θ cos φ + sin θ sin φ

tan(θ - φ) = (tan θ - tan φ) / (1 + tan θ tan φ)

Use unit circle and cosine rule for derivation.

sin(75°) = sin(45°)cos(30°) + cos(45°)sin(30°)

They simplify calculations in trigonometry problems.

It equals sin(50°) using the sine sum identity.