Help needed on trigonometry identities.

Question

Equation 1: a₂sinθ₂ = a₃sinθ₃ - a₁sinθ₁

Equation 2: a₂cosθ₂ = a₄ - a₁cosθ₁ + a₃cosθ₃

Answer: a₂² = a₁² + a₃² + a₄² - 2a₁a₃sinθ₁sinθ₃ - 2a₁a₄cosθ_{1 +} 2a₃a₄cosθ₃ - 2a₁a₃cosθ₁cosθ₃

What is the method to get to the answers?

Answer 1

1. From a₂sinθ₂ = a₃sinθ₃ - a₁sinθ_1, take a square on both side, we get

(a₂sinθ₂₎² = (a₃sinθ₃ - a₁sinθ₁₎²

1. From a₂cosθ₂ = a₄ - a₁cosθ₁ + a₃cosθ_3, take a square on both side, we get

(a₂cosθ₂₎² = (a₄ - a₁cosθ₁ + a₃cosθ₃₎²

1. Add the two equations together, you will get the answer