Question

A square with each side equal to \( a \) lies above the \( x \)-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle \( \alpha \) (\( 0 < \alpha < \frac{\pi}{4} \)) with the positive direction of the \( x \)-axis. The equation of the diagonals of the square is:

• A. \( y(\cos \alpha - \sin \alpha) = x(\sin \alpha + \cos \alpha) \)
• B. \( y(\cos \alpha + \sin \alpha) = x(\cos \alpha - \sin \alpha) \)
• C. \( y(\sin \alpha + \cos \alpha) + x(\cos \alpha - \sin \alpha) = a \)
• D. \( y(\cos \alpha - \sin \alpha) + x(\cos \alpha + \sin \alpha) = a \)

Hint:

For problems involving geometric shapes, use symmetry and coordinate geometry to derive the required equations.