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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

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

Grade:12

1 Answers

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
10 years ago

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

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