Q. 185.0( 1 Vote )

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

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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