If the lines \( 2(\sin a+\sin b) x-2 \sin (a-b) y=3 \) and \( 2(\co...
If the lines \( 2(\sin a+\sin b) x-2 \sin (a-b) y=3 \) and \( 2(\cos a+\cos b) x+2 \cos (a-b) y=5 \) are perpendicular, then \( \sin 2 a+\sin 2 b \) is equal to
(a) \( \sin (a-b)-2 \sin (a+b) \)
(b) \( \sin 2(a-b)-2 \sin (a+b) \)
(c) \( 2 \sin (a-b)-\sin (a+b) \)
(d) \( \sin 2(a-b)-\sin (a+b) \)
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