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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 sinα+sinβ=−2165,cosα+cosβ=−2765Now(sinα+sinβ)2+(cosα+cosβ)2=(−2165)2+(−2765)2⇒2+2sinαsinβ+2cosαcosβ=441652+729652⇒2+2[cos(α−β)]=1170(65)2⇒2.2cos2(α+β2)=1170(65)2⇒cos(α−β2)=3√130130=3√130Thereforecos(α−β2)=−3√130,{∵π2<α−β2<3π2}.