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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