If the sides a, b, c of the triangle ABC are | vedclass

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(B) Given that $a, b, c$ are in harmonic progression,we have $1/a, 1/b, 1/c$ in arithmetic progression. Using the formula $\operatorname{cosec}^2(A/2)

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Arithmetic progression

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(B) Given that $a, b, c$ are in harmonic progression,we have $1/a, 1/b, 1/c$ in arithmetic progression. Using the formula $\operatorname{cosec}^2(A/2) = \frac{bc}{(s-b)(s-c)}$,where $s = \frac{a+b+c}{2}$,we can express the terms. Since $s-a = \frac{b+c-a}{2}$,$s-b = \frac{a+c-b}{2}$,and $s-c = \frac{a+b-c}{2}$,the expression $\operatorname{cosec}^2(A/2)$ simplifies to $\frac{bc}{s(s-a)} 	imes \frac{s(s-a)}{(s-b)(s-c)}$. More directly,$\operatorname{cosec}^2(A/2) = \frac{bc}{\Delta^2} s(s-a)$. For $a, b, c$ in harmonic progression,$b = \frac{2ac}{a+c}$. Substituting this into the expressions for the angles,it can be shown that the terms $\operatorname{cosec}^2(A/2), \operatorname{cosec}^2(B/2), \operatorname{cosec}^2(C/2)$ form an arithmetic progression.

If the sides $a, b, c$ of the triangle $ABC$ are in harmonic progression,then $\operatorname{cosec}^2(A/2), \operatorname{cosec}^2(B/2), \operatorname{cosec}^2(C/2)$ are in

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