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Question

If a=cos α cos β+sin α sin β cos γ, b=cos α sin βsin α cos β cos γ and c=sin α sin γ then a2+b2+c2 is equal to


A

-1

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B

0

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C

1

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D

None of these

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Solution

The correct option is C

1


a2+b2+c2=cos2 α(cos2 β+sin2 β)+sin2 α cos2 α (sin2 α+cos2 β)+sin2 α sin2γ=1


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