Question

If acoso - b sin 0 = c, prove that a sin 0 + b cos 0 = √a^2+b^2-c^2​

Answer 1

We have to equations

• acos∅ - bsin∅ = c

Now, let bcos∅ + asin∅ = x

On squaring both equations,

→ a²cos²∅ + b²sin²∅ - 2ab cos∅sin∅ = c²

→ b²cos²∅ + a²sin²∅ + 2ab cos∅sin∅ = x²

Adding both equations we get,

→ a²cos²∅ + b²sin²∅ + b²cos² + a²sin²∅ = c² + x²

→ (a² + b²)cos²∅ + (a² + b²)sin²∅ = c² + x²

→ (a² + b²)(cos²∅ + sin²∅) = c² + x²

→ a² + b² - c² = x²

→ √(a² + b² - c²) = asin∅ + bcos∅

Hence Proved