wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In any ΔABC sinAsinB+sinCsinA3 then show that the equality holds if and only if triangle is equilateral.

Open in App
Solution

We know that
asinA=bsinB=csinC ...(sine rule).

Substituting in the above expression, we get

ab+ca+ba+cb+ca+bc

Now if it is an equilateral triangle,
a=b=c

Hence the above expression reduces to

ab+ca+ba+cb+ca+bc
=3[aa+aa]

=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
De Moivre's Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon