Question

If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a² + b² =
A. m²− n²
B. m²n²
C. n²− m²
D. m² + n²

Answer 1

Answer:

the answer will be m²+n²

Answer 2

D. m² + n²

Step-by-step explanation:

Given:

a cos θ + b sin θ = m

a sin θ − b cos θ = n

m² + n² = (a cos θ + b sin θ)² + (a sin θ − b cos θ)²

 = a²cos²θ + b²sin²θ + 2ab.sinθ.cosθ + a²sin²θ + b²cos²θ - 2ab.sinθ.cosθ

 = a²cos²θ + b²sin²θ + a²sin²θ + b²cos²θ

 = a² (cos²θ + sin²θ) + b²(sin²θ + cos²θ)

 = a² (1) + b² (1)

m² + n² = a² + b²  

Option D is the answer.