(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$. The expression is $E = a \cos^2\left(\frac{C}{2}\right) + c \cos^2\left(\frac{A}{2}\right

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(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$. The expression is $E = a \cos^2\left(\frac{C}{2}\right) + c \cos^2\left(\frac{A}{2}\right)$. Using the identity $2 \cos^2\theta = 1 + \cos(2\theta)$,we get: $E = \frac{a}{2}(1 + \cos C) + \frac{c}{2}(1 + \cos A)$ $E = \frac{1}{2}(a + a \cos C + c + c \cos A)$ By the projection formula,$a \cos C + c \cos A = b$. $E = \frac{1}{2}(a + c + b)$ Since $a + c = 2b$,we have: $E = \frac{1}{2}(2b + b) = \frac{3b}{2}$.

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

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In $\triangle ABC$,with usual notations,if $a, b, c$ are in $A.P.$,then $a \cos^2\left(\frac{C}{2}\right) + c \cos^2\left(\frac{A}{2}\right) = $

MHT CET 2018 All MHT CET

A
$\frac{3a}{2}$
B
$\frac{3c}{2}$
C
$\frac{3b}{2}$
D
$\frac{3abc}{2}$

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

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In $\triangle ABC$,with usual notations,if $a, b, c$ are in $A.P.$,then $a \cos^2\left(\frac{C}{2}\right) + c \cos^2\left(\frac{A}{2}\right) = $

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