What will be the solution of the mentioned problem??

If,A+B+C=piandcotA+cotB+cotC=sqrt3,If,A+B+C=πandcotA+cotB+cotC=3,
then show that,color(blue)(A=B=C).A=B=C.

1 Answer
Jan 12, 2018

We can show it in the following way.
Given A+B+C=piA+B+C=π

  1. First assumption: We are discussing three angles A,B and CA,BandC of a triangle.
  2. If A=B=C=>DeltaABC is an equilateral triangle.
  3. All angles of an equilateral triangle are equal and each =60^@

Now

cotA+cotB+cotC=cot60^@+cot60^@+cot60^@
=3cot60^@=3xx1/sqrt3=sqrt3
Which is =RHS of the given equation.

Hence our assumption and its following results are true.
Hence proved.