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Question

Let α,β be such that 0<αβπ<2π. if sinα+sinβ=2165 and cosα+cosβ=2765. Then the value of cos αβ2 is a

A
665
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B
3130
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C
3130
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D
665
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Solution

The correct option is B 3130
(sinα+sinβ)2+(cosα+cosβ)2
2+2cos(αβ)=1865
cos2αβ2=9130,Asπ<αβ<3ππ2<αβ2<3π2
cosαβ2=3130

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