Question

If \( x + y = 2 \cos \theta + 5 \sin \theta \), then \( x^2 + y^2 \) is equal to?

• A. \( 3x - 4y \)
• B. \( 4x - 3y \)
• C. \( 3x + 4y \)
• D. None of these

Hint:

When given a trigonometric equation involving sums of variables, square both sides to find the sum of squares.

Answer 1

The Correct Option is B

By squaring the given equation \( x + y = 2 \cos \theta + 5 \sin \theta \) and simplifying, the equation for \( x^2 + y^2 \) is derived, and the correct answer is \( 4x - 3y \).