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Question

If cosαcosβ=m and cosαsinβ=n, prove that (m2+n2)cos2β=n2.

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Solution

cosαcosβ=m and cosαsinβ=n
(m2+n2)cos2β
=(cos2αcos2β+cos2αsin2β).cos2β
=(cos2α.sin2β+cos2α.cos2βsin2β)
=cos2α(sin2β+cos2βsin2β)
=cos2αsin2β
=n2

Hence, proved.

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