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Ajay Kumar Grade: 11
        The expression cos^2 q + cos^2 (a+q) - 2 cos a cosq cos (a+q) is independent of

(A) q
(b) a
(C) both a and q
(D)none of a and q
6 years ago

Answers : (1)

Fawz Naim
37 Points
										

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


 

6 years ago
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