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cos^2 q+cos^2(a+q)-2cosa.cosq.cos(a+q)
cos^2 q+cos(a+q)[cos(a+q)-2cosa.cosq]
cos^2 q+cos(a+q)[cosa.cosq-sina.sinq-2cosa.cosq]
cos^2 q+cos(a+q)[-cosa.cosq-sina.sinq]
cos^2 q-cos(a+q)[cosa.cosq+sina.sinq]
cos^2 q-cos(a+q).[cos(a-q)]
cos^2 q-[2cos(a+q).cos(a-q)/2]
cos^2 q-[cos2a+cos2q/2]
2cos^2 q-cos2a-cos2q/2
2cos^2 q-(cos^2 a-sin^2 a)-(cos^2 q-sin^2 q)/2
2cos^2 q-cos^2 a+sin^2 a-cos^2q+sin^2 q/2
cos^2 q+sin^2 q-cos^2 a+sin^2 a/2
1-cos^2 a+sin^2 a/2
therefore it is independent of q.So option (A) is correct
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