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Question

If cosx+cosy=a and sinx+siny=b then find the value of cos(xy).

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Solution

Given,cosx+cosy=a.....(1) and sinx+siny=b......(2).
Now squaring (1) and (2) and then adding we get,
(cosx+cosy)2+(sinx+siny)2=a2+b2
or, (sin2x+cos2x)+(sin2y+cos2y)+2(cosx.cosy+sinx.siny)=a2+b2
or, 2cos(xy)=(a2+b22)
or, cos(xy)=(a2+b22)2

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