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A square of side $a$ lies above the $x$-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha ( 0 < \alpha < \frac{\pi}{4})$ with the positive direction of $x$-axis. The equation of its diagonal not passing through the origin is :

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

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