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Question

Let α, β be such that π<αβ<3π.Ifsin α+sin β=2165 and cos α+cos β=2765,then the value of cosαβ2 is


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 C
sin α+sin β=2165, cos α+cos β=2765Now (sin α+sin β)2+(cos α+cos β)2=(2165)2+(2765)22+2 sin α sin β+2 cos α cos β=441652+7296522+2[cos(αβ)]=1170(65)22.2 cos2(α+β2)=1170(65)2cos(αβ2)=3130130=3130Therefore cos(αβ2)=3130,{π2<αβ2<3π2}.

Mathematics

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