(A) Given,$\cos A + \cos B + \cos C = \frac{3}{2}$.We know that for any triangle $ABC$,the maximum value of $\cos A + \cos B + \cos C$ is $\frac{3}{2}

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(A) Given,$\cos A + \cos B + \cos C = \frac{3}{2}$.We know that for any triangle $ABC$,the maximum value of $\cos A + \cos B + \cos C$ is $\frac{3}{2}$,which occurs if and only if $A = B = C = 60^{\circ}$ or $\frac{\pi}{3}$ radians.Since $A = B = C = \frac{\pi}{3}$,all three angles are equal.Therefore,$\triangle ABC$ is an equilateral triangle.Hence,option $A$ is correct.

Class 11 Mathematics Trigonometrical Equations Relation between sides and angles, Solutions of triangles

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Let $A, B$ and $C$ be three angles of a $\triangle ABC$ such that $\cos A + \cos B + \cos C = \frac{3}{2}$,then the $\triangle ABC$ is

AP EAMCET 2020 All AP EAMCET

A
Equilateral
B
Right angled
C
Isosceles but not equilateral
D
Scalene

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