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if cosx+cosy+cosz=0=sinx+siny+sinz=0 then find cos(x-y)+cos(y-z)+cos(z-x)

Piyush Raj , 5 Years ago
Grade 11
anser 1 Answers
Arun

Last Activity: 5 Years ago

cos (x-y) + cos (y-z) + cos (z-x) = -3/2
=3+2(cos (x-y) + cos (y-z) + cos (z-x))=0
=1+1+1+2(cos (x-y) + cos (y-z) + cos (z-x))=0
=(sin2x + cos2x) + (sin2y + cos2y) + (sin2z + cos2z) + 2(cosx cosy + sinx siny + cosy cosz + siny sinz + cosz cosx + sinz sinx)=0
=(sin2x + sin2y + sin2z+2(sinx siny + siny sinz + sinz sinx))+(cos2x + cos2y + cos2z +2(cosx cosy + cosy cosz + cosz cosx))=0
=(sinx + siny + sinz)2 + (cosx + cosy + cosz)2=0
only and only iff
sinx + siny + sinz=0
cosx + cosy + cosz=0

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