(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}

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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

Medium

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

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Relation between sides and angles, Solutions of triangles

Previous Year

AP EAMCET 2020 Paper All AP EAMCET years →

If in triangle $ABC$,with usual notations $\sin \frac{A}{2} \cdot \sin \frac{C}{2} = \sin \frac{B}{2}$ and $2s$ is the perimeter of the triangle,then the value of $s$ is

MediumMHT CET 2025

View Solution

In a triangle $ABC$,if $a = 2$,$B = 60^\circ$ and $C = 75^\circ$,then $b =$

Easy

View Solution

In $\triangle ABC$,with the usual notations,if $\sin B \sin C = \frac{bc}{a^2}$,then the triangle is $\ldots$.

EasyMHT CET 2019

View Solution

The base of a triangle is $80$ and one of the base angles is $60^{\circ}$. If the sum of the lengths of the other two sides is $90$,then the shortest side is of length

MediumAP EAMCET 2017

View Solution

If $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B$,then $A, B, C$ are in

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

If in triangle $ABC$,with usual notations $\sin \frac{A}{2} \cdot \sin \frac{C}{2} = \sin \frac{B}{2}$ and $2s$ is the perimeter of the triangle,then the value of $s$ is

In a triangle $ABC$,if $a = 2$,$B = 60^\circ$ and $C = 75^\circ$,then $b =$

In $\triangle ABC$,with the usual notations,if $\sin B \sin C = \frac{bc}{a^2}$,then the triangle is $\ldots$.

The base of a triangle is $80$ and one of the base angles is $60^{\circ}$. If the sum of the lengths of the other two sides is $90$,then the shortest side is of length

If $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B$,then $A, B, C$ are in

Vedclass Test Series

Exam Paper Generator

Online Exam Module