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Question

sin2α+cos2(α+β)+2sinα.sinβcos(α+β)=

A
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B
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C
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D
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Solution

The correct option is D
G.E = sin2α+cos(α+β)[cos(α+β)+2sinαsinβ]
= sin2α+cos(α+β)[cosαcosβsinαsinβ+2sinαsinβ]
= sin2α+cos(α+β)[cos(αβ)]=sin2α+cos2βsin2α=cos2β

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