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Question

(cosα+cosβ)2+(sinα+sinβ)2= kcos2(αβ2), then k is equal to

A
4
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B
3
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C
2
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D
1
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Solution

The correct option is A 4
LHS=(cos2α+cos2β+2cosαcosβ)+(sin2α+sin2β+2sinαsinβ)
=2+2(cosαcosβ+sinαsinβ)
=2+2cos(αβ)
=4cos2αβ2

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