if |z|=1, z1, z2, z3 be any 3 points on that circle.if $1,$2,$3 be the arguments of z1,z2 and z3 respectively, then cos($1-$2)+cos($2-$3)=cos($3-!) is.....................hint: min value

Hii Naidu

First thing...Question is something like this ....

cos ( $1 - $2 ) + cos ( $2 - $3) + cos ( $3-$1) = ?

Now cos is a decreasing function....so when you need to find the minimum value..then you must give the maximum angle ..

i.e cos x = max ....if x is min

or cos x = min ...if x is max...

So if we want to find out the minimum value of cos ( $1 - $2 ) + cos ( $2 - $3) + cos ( $3-$1) ...then each

$1 - $2   $2 - $3 and $3 - $1   must be minimum....

So the one logic is ..the all three points ..Z1 Z2 Z3 lies on circle as the vertex of Equilateral triangle ...means if you will join the Z1 Z2 and Z3 you will get equilateral triangle....

SO in this case $1 - $2 =  $2 - $3 = $3 - $1 = 120

So cos ( $1 - $2 ) + cos ( $2 - $3) + cos ( $3-$1)  = -3/2  ans

Regards

Yagya

askiitians_expert