# In ∆ABC, if cosAa=cosBb, then show that it is an isosceles triangle - Mathematics and Statistics

Sum

In ∆ABC, if (cos "A")/"a" = (cos "B")/"b", then show that it is an isosceles triangle

#### Solution

In ∆ABC by sine rule, we have

"a"/"sin A" = "b"/"sin B" = "k"

∴ a = k sin A, b = k sin B

Now, (cos "A")/"a" = (cos "B")/"b"    .......[Given]

∴ "cos A"/"k sin A" = "cos B"/"k sin B"

∴ "cos A"/"sin A" = "cos B"/"sin B"

∴ sin A cos B = cos A sin B

∴ sin A cos B − cos A sin B = 0

∴ sin (A − B) = 0 = sin 0

∴ A − B = 0

∴ A = B

Hence, ∆ABC is an isosceles triangle.

Concept: Solutions of Triangle
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