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Question

If a=cosαcosβ+sinαsinβcosγ
b=cosαsinβsinαcosβcosγ
and c=sinαsinγ, then a2+b2+c2 is equal to

A
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B
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C
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D
none of these
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Solution

The correct option is C 1
Given a=cosαcosβ+sinαsinβcosγ
b=cosαsinβsinαcosβcosγ
and c=sinαsinγ

Consider, a2+b2+c2=cos2αcos2β+sin2αsin2βcos2γ+2cosαcosβsinαsinβcosγ+cos2αsin2β+cos2βsin2αcos2γ2cosαcosβsinαsinβcosγ+4sin2αsin2γ

a2+b2+c2=cos2α+sin2αcos2γ+4sin2αsin2γ

a2+b2+c2=1+3c2

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