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Question

cosα+cosβsinα+sinβ+sinαsinβcosαcosβ=

A
1
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B
2
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C
2
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D
0
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Solution

The correct option is B 0
cosα+cosβsinα+sinβ+sinαsinβcosαcosβ
= cos2αcos2β+sin2αsin2β(sinαsinβ)(cosαcosβ)
= (cos2α+sin2α)(cos2β+sin2β)(sinαsinβ)(cosαcosβ)
= 11(sinαsinβ)(cosαcosβ) (Since, cos2θ+sin2θ=1)
= 0

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