Question

If a cos θ − b sin θ = c, then a sin θ + b cos θ =
A. +-√a²+b²+c²
B. +-√a²+b²-c²
C. +-√c²-a²+b²
D. None of these

Answer 1

Answer:

options D is the right answer

Answer 2

B. +-√a²+b²-c²

Step-by-step explanation:

Given: a sin θ - b cos θ = c

Then (a sinθ + b cosθ)² + (a cosθ - b sinθ)²

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

= a²sin²θ + a²cos²θ +  b²sin²θ + b²cos²θ  

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

= a² + b²

(a sinθ + b cosθ)² + (a cosθ - b sinθ)² = a² + b²

(a sinθ + b cosθ)² + c² = a² + b²

(a sinθ + b cosθ)² = a²+b²-c²

a sinθ + b cosθ = +_√a²+b²-c²

Option B is the answer.