(C) The given expression is $E = a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$. Expanding the terms,we get: $E = ab^2\cos A + ac^2\cos

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(C) The given expression is $E = a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$. Expanding the terms,we get: $E = ab^2\cos A + ac^2\cos A + bc^2\cos B + ba^2\cos B + ca^2\cos C + cb^2\cos C$. Grouping the terms: $E = ab(b\cos A + a\cos B) + bc(c\cos B + b\cos C) + ca(a\cos C + c\cos A)$. Using the projection formula $c = b\cos A + a\cos B$,$a = c\cos B + b\cos C$,and $b = a\cos C + c\cos A$: $E = ab(c) + bc(a) + ca(b) = abc + abc + abc = 3abc$.

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

Medium

In any triangle $ABC$,the value of $a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$ is

A
$3abc^2$
B
$3a^2bc$
C
$3abc$
D
$3ab^2c$

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Trigonometrical Equations

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

The set of solutions of the system of equations $x+y = \frac{2 \pi}{3}$ and $\cos x + \cos y = \frac{3}{2}$,where $x, y$ are real,is

DifficultAP EAMCET 2013

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In $\triangle ABC$,if $B=90^{\circ}$,then $2(r+R)=$

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The common roots of the equations $2\sin^2 x + \sin^2 2x = 2$ and $\sin 2x + \cos 2x = \tan x$ are

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In $\triangle ABC$,if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$ and side $a=2$,then the area of the $\triangle ABC$ (in sq. units) is

EasyTS EAMCET 2023

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Let the angles $A, B, C$ of a triangle $ABC$ be in arithmetic progression. If the exradii $r_1, r_2, r_3$ of triangle $ABC$ satisfy the condition $r_3^2 = r_1 r_2 + r_2 r_3 + r_3 r_1$, then $b =$

DifficultTS EAMCET 2025

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In any triangle $ABC$,the value of $a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$ is

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