Q. 185.0( 1 Vote )

In a ΔABC, if prove that the triangle is isosceles.

Answer :


The key point to solve the problem:


To prove a triangle isosceles our task is to show either any two angles equal or two sides equal.


Idea of cosine formula - Cos C =


The idea of sine Formula:



Given,


As it has sin terms involved so that sine formula can work, and cos C is also there so we might need cosine formula too.


Let’s apply sine formula keeping a target to prove any two sides equal.


Using sine formula we have –



sin A = ak and sin B = bk


cos C =


If we apply cosine formula, we will get an equation in terms of sides only that may give us any two sides equal.


Using, Cos C =


We have,



b2 + a2 – c2 = a2


b2 = c2


b = c


Hence 2 sides are equal.


Δ ABC is isosceles. ….proved


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