If a cos θ + b sin θ = m and a sin θ - b cos θ = n, prove that

1.	If a cos θ + b sin θ = m and a sin θ - b cos θ = n, prove that m2 + n2 = a2 + b2
Answer» Given, m² = a² cos² θ + 2 ab sin θ cos θ + b² sin²θ and n² = a² sin² θ-2 ab sin θ cos θ + b²cos² θ Adding equations (i) and (ii) m² + n² = a² (cos² θ + sin² θ) + b²(cos²θ + sin² θ) = a² (1) + b² (1) = a² + b² = RHS

If a cos θ + b sin θ = m and a sin θ - b cos θ = n, prove that m2 + n2 = a2 + b2

Answer»

Given,

m² = a² cos² θ + 2 ab sin θ cos θ + b² sin²θ

and

n² = a² sin² θ-2 ab sin θ cos θ + b²cos² θ

Adding equations (i) and (ii)

m² + n² = a² (cos² θ + sin² θ) + b²(cos²θ + sin² θ)

= a² (1) + b² (1)

= a² + b² = RHS