Question

If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x² + y² = ____________.

Options

• 34

• 12

• 8

• 17

Answer 1

If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x² + y² = 34.

Explanation:

Given, x cos θ + y sin θ = 5

and x sin θ − y cos θ = 3

Squaring and adding, we get

x² cos² θ + y² sin² θ + 2xy sin θ cos θ + x² sin² θ + y² cos² θ − 2xy sinθ cos θ = 25 + 9

x² (cos² θ + sin² θ) + y² (sin² θ + cos² θ) = 34

x² + y² = 34