Question

if x=y cos(2π/3)=z cos(4π/3) then xy+yz+xz=

Answer 1

Let x = y cos 2pie by 3=z cos 4pie by 3 =k Then k/x = 1 ------(a) k/y = cos 2pie by 3 -------(b) k/z = cos 4pie by 3 -------(c)Now by adding (a) , (b) and (c) [k (yz + xz + xy)]/xyz = 1 + cos 2pie by 3 +cos 4pie by 3Taking L.C.M we get k (yz) + k (xz) + k (xy) = 1 + cos 2pie by 3 +cos 4pie by 3Now putting values of (cos 2pie by 3 ) and (cos 4pie by 3) we get[k (yz + xz + xy)]/xyz = 1-(1/2)-(1/2)Then[k (yz + xz + xy)]/xyz = 0k (yz + xz + xy) = 0yz + xz + xy = 0