(B) Using the Sine Rule,we have $a = 2R \sin A$ and $b = 2R \sin B$.Substituting these into the given equation $a \cos B = b \cos A$:$(2R \sin A) \cos

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(B) Using the Sine Rule,we have $a = 2R \sin A$ and $b = 2R \sin B$.Substituting these into the given equation $a \cos B = b \cos A$:$(2R \sin A) \cos B = (2R \sin B) \cos A$$\sin A \cos B = \sin B \cos A$$\sin A \cos B - \cos A \sin B = 0$$\sin(A - B) = 0$Since $A$ and $B$ are angles of a triangle,$A - B = 0$,which implies $A = B$.Therefore,the triangle is an isosceles triangle.

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

Easy

In any $\Delta ABC$,if $a \cos B = b \cos A$,then the triangle is

A
Equilateral triangle
B
Isosceles triangle
C
Scalene triangle
D
Right-angled triangle

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Equations

Subtopic

Relation between sides and angles, Solutions of triangles

If $R : r_1 : r = 5 : 12 : 2$, then $r + r_3 + r_2 - r_1 = $

DifficultTS EAMCET 2020

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In triangle $ABC$,if $\angle A = 45^\circ$ and $\angle B = 75^\circ$,then $a + c\sqrt{2} = $

MediumIIT 1988

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In $\triangle ABC$,if $b+c : c+a : a+b = 7 : 8 : 9$,then the smallest angle (in radians) of that triangle is

MediumAP EAMCET 2024

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If the sides of a triangle are in the ratio $3 : 7 : 8,$ then $R : r$ is equal to

Medium

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In $\triangle ABC$,if $\frac{1}{r_1}, \frac{1}{r_2}$ and $\frac{1}{r_3}$ are in arithmetic progression,then $r_2 : r =$

DifficultAP EAMCET 2023

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In any $\Delta ABC$,if $a \cos B = b \cos A$,then the triangle is

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If $R : r_1 : r = 5 : 12 : 2$, then $r + r_3 + r_2 - r_1 = $

In triangle $ABC$,if $\angle A = 45^\circ$ and $\angle B = 75^\circ$,then $a + c\sqrt{2} = $

In $\triangle ABC$,if $b+c : c+a : a+b = 7 : 8 : 9$,then the smallest angle (in radians) of that triangle is

If the sides of a triangle are in the ratio $3 : 7 : 8,$ then $R : r$ is equal to

In $\triangle ABC$,if $\frac{1}{r_1}, \frac{1}{r_2}$ and $\frac{1}{r_3}$ are in arithmetic progression,then $r_2 : r =$

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