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\operatorname { cos } x + \operatorname { cos } y + \operatorname { cos } z = \operatorname { sin } x + \operatorname { sin } y + \operatorname { sin } z = 0 , \text { show that } \operatorname { cos } \frac { x - y } { 2 } |
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Answer» cosx + cosy = -cosz , cos^2x + cos^2y + 2cosx.cosy = cos^2z , in a similar way : sin^2x+sin^2y+2sinx.siny = sin^2z , add eqns & simplify : 1+1+2(cosx.cosy+sinx.siny) = 1 , 2cos(x-y)=1-2=-1 , cos(x-y)=-1/2 |
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