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Question

Let α and β be such that π<αβ<2π. If sinα+sinβ=2165 and cosα+cosβ=1765, then the value of cosαβ2 is

A
4130
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B
3130
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C
665
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D
None of these
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Solution

The correct option is C None of these
π<αβ<2ππ2<αβ2<πcos(αβ2)<0
sinα+sinβ=2165 ...(1)
cosα+cosβ=1765 ...(2)
Squaring and adding (1) & (2)
1+1+2(sinαsinβ+cosαcosβ)=(2165)2+(1765)22(1+cos(αβ))=(2165)2+(1765)2cos2(αβ2)=7304(65)2
cos(αβ2)=730130 ...{ cos(αβ2)<0}

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