What will be the solution of the mentioned problem??
#If,A+B+C=piandcotA+cotB+cotC=sqrt3,#
then show that,#color(blue)(A=B=C).#
then show that,
1 Answer
Jan 12, 2018
We can show it in the following way.
Given
- First assumption: We are discussing three angles
#A,B and C# of a triangle. - If
#A=B=C=>DeltaABC# is an equilateral triangle. - 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.
