(D) Given $a \cos A = b \cos B$. Using the sine rule,$a = 2R \sin A$ and $b = 2R \sin B$. Substituting these,we get $2R \sin A \cos A = 2R \sin B \cos

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(D) Given $a \cos A = b \cos B$. Using the sine rule,$a = 2R \sin A$ and $b = 2R \sin B$. Substituting these,we get $2R \sin A \cos A = 2R \sin B \cos B$. $\Rightarrow \sin 2A = \sin 2B$. This implies $2A = 2B$ or $2A = \pi - 2B$. $\Rightarrow A = B$ or $A + B = \frac{\pi}{2}$. If $A = B$,the triangle is isosceles. If $A + B = \frac{\pi}{2}$,then $C = \pi - (A + B) = \frac{\pi}{2}$,so the triangle is right-angled. Therefore,the triangle is right-angled or isosceles.

Class 11 Mathematics Trigonometrical Equations Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

If $a \cos A = b \cos B$,then $\Delta ABC$ is

A
isosceles only
B
right angled only
C
equilateral
D
right angled or isosceles

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Trigonometrical Equations

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Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

Let $\alpha$ and $\beta$ be two distinct roots of $a \cos \theta + b \sin \theta = c$, where $a, b, c$ are three real constants and $\theta \in [0, 2\pi]$. Then, $\alpha + \beta$ is also a root of the same equation, if

MediumWBJEE 2015

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If $\Delta$ denotes the area of triangle $ABC$,then $(b \sin C + c \sin B)(b \cos C + c \cos B) =$

EasyTS EAMCET 2022

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In a triangle $PQR$ with usual notations,$\angle R = \frac{\pi}{2}$. If $\tan \frac{P}{2}$ and $\tan \frac{Q}{2}$ are the roots of the equation $ax^2 + bx + c = 0$ $(a \neq 0)$,then:

MediumMHT CET 2025

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In $\triangle ABC$,find the value of $r r_1 \cot \frac{A}{2} + r r_2 \cot \frac{B}{2} + r r_3 \cot \frac{C}{2}$.

MediumAP EAMCET 2024

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In $\triangle ABC$,if $a, b, c$ are $5, 12$ and $13$ respectively,then $b^2 \sin 2C + c^2 \sin 2B =$

MediumAP EAMCET 2023

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Let $\alpha$ and $\beta$ be two distinct roots of $a \cos \theta + b \sin \theta = c$, where $a, b, c$ are three real constants and $\theta \in [0, 2\pi]$. Then, $\alpha + \beta$ is also a root of the same equation, if

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