In a triangle ABC if A2B2-c-B2C2-a and C2A2-b then 1s-a-1s-b-1s-c-

Given: A2B2=c ⇒ nbsp; (s)(s a)Δ×(s)(s b)Δ=c ⇒1s c=cs⋯(i) Similarly, ⇒1s b=bs⋯(ii) Similarly, ⇒1s a=as⋯(iii) Adding (i),(ii),(iii) ⇒∑1s c=∑cs ⇒∑1s c= a+b+cs = ...

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Standard XII

Physics

1st Law of Thermodynamics

In a triangle...

Question

In a triangle $A B C$ if $cot \frac{A}{2} cot \frac{B}{2} = c, cot \frac{B}{2} cot \frac{C}{2} = a and cot \frac{C}{2} cot \frac{A}{2} = b$ then $\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} =$

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Solution

The correct option is D $2$
Given: $cot \frac{A}{2} cot \frac{B}{2} = c$
$\Rightarrow \frac{(s) (s - a)}{Δ} \times \frac{(s) (s - b)}{Δ} = c$
$\Rightarrow \frac{1}{s - c} = \frac{c}{s} \dots (i)$
Similarly,
$\Rightarrow \frac{1}{s - b} = \frac{b}{s} \dots (i i)$
Similarly,
$\Rightarrow \frac{1}{s - a} = \frac{a}{s} \dots (i i i)$
Adding $(i), (i i), (i i i)$
$\Rightarrow \sum \frac{1}{s - c} = \sum \frac{c}{s}$
$\Rightarrow \sum \frac{1}{s - c} = \frac{a + b + c}{s} = \frac{2 s}{s} = 2$

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Similar questions

Q. In a triangle

A B C,

cot (\frac{A}{2}) cot (\frac{B}{2}) = c,

cot (\frac{B}{2}) cot (\frac{C}{2}) = a,

and

cot (\frac{C}{2}) cot (\frac{A}{2}) = b

, then

\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} =

Q. In

Δ A B C

cot \frac{A}{2} . cot \frac{B}{2} = c; cot \frac{B}{2} cot \frac{C}{2} = a;

and

cot \frac{C}{2} cot \frac{A}{2} = b

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\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} =

Q. In

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cot \frac{A}{2} \cdot cot \frac{B}{2} = c

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and

cot \frac{C}{2} \cdot cot \frac{A}{2} = b

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\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} =

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In a triangle ABC if cotA2cotB2=c,cotB2cotC2=a and cotC2cotA2=b then 1s−a+1s−b+1s−c=

The correct option is D 2Given: cotA2cotB2=c ⇒(s)(s−a)Δ×(s)(s−b)Δ=c ⇒1s−c=cs⋯(i) Similarly, ⇒1s−b=bs⋯(ii) Similarly, ⇒1s−a=as⋯(iii) Adding (i),(ii),(iii) ⇒∑1s−c=∑cs ⇒∑1s−c=a+b+cs=2ss=2

In a triangle $A B C$ if $cot \frac{A}{2} cot \frac{B}{2} = c, cot \frac{B}{2} cot \frac{C}{2} = a and cot \frac{C}{2} cot \frac{A}{2} = b$ then $\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} =$