Question

If 4sin theta+3 cos theta=m,4cos theta-3 sin theta =n...then find the value of m^2+n^2??​

Answer 1

Answer:

m²+n² = 25  or m²+n² = 5²

Step-by-step explanation:

given, m = 4sinθ + 3cosθ

   and n = 4cosθ - 3sinθ

so, m²+n² = (4sinθ + 3cosθ)² + (4cosθ - 3sinθ)²

                = 16sin²θ + 24sinθcosθ + 9cos²θ + 16cos²θ - 24sinθcosθ + 9sin²θ

                = 16sin²θ + 16cos²θ  + 9cos²θ + 9sin²θ

                = 16 (sin²θ +cos²θ)  + 9 (cos²θ + sin²θ)

                = 16 (1)  + 9 (1)

                = 16 + 9

                = 25

=> m²+n² = 25