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Area of given ∆ ABC = √3 .
Solution →
Given that -
→CosA/a = CosB/b = CosC/c ....1st
And according to sine formula, we know that.
→a/SinA= b/SinB = c/SinC .......2nd
Now multiplying equation 1st and 2nd -
→ CosA/SinA = CosB/SinB = CosC/SinC.
We know that Cos A/sinA = cotA similarly-
→ CotA = cotB = cot C
It implies that all angles of the given ∆ABC are equivalent.
So, A = B= C = 60°
So this is equilateral triangle .
Now Area of equilateral triangle =
√3 a²/4.
And given that side of triangle is 2 .
So, √3 × 2²/ 4
Area = √3
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