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In a \Delta ABC\: \cot \frac{A}{2}\cdot\cot \frac{B}{2}\cdot\cot \frac{C}{2} is equal to

Option: 1

\frac{\Delta }{r^{2}}
 

 


Option: 2

\frac{(a+b+c)^{2} }{abc}.2R


Option: 3

\frac{\Delta }{r}

 


Option: 4

\frac{\Delta }{Rr}


Answers (1)

best_answer

 

Trigonometric Ratios of Functions -

cosec\ \Theta = \frac{Hyp}{Opp}

\sec \Theta = \frac{Hyp}{Base}

\cot \Theta = \frac{Base}{Opp}

- wherein

Trigonometric Ratios of Functions 2

 

 

\cot \frac{A}{2}\cdot\cot \frac{B}{2}\cdot\cot \frac{C}{2}

=\frac{s(s-a)}{\Delta }\cdot\frac{s(s-b)}{\Delta }\cdot\frac{s(s-c)}{\Delta }

=\frac{s^3(a+b+c)}{\Delta^3 }=\frac{s^2\Delta^2 }{\Delta^3}=\frac{s^{2}}{\Delta }

=\left ( \frac{\Delta^2}{r^2} \right )\times \frac{1}{\Delta}=\frac{\Delta}{r^2}\; \; \; \; \; \; \; \; \; \; [\because s=\frac{\Delta}{r}]

\cot \frac{A}{2}\cdot\cot \frac{B}{2}\cdot\cot \frac{C}{2}=\frac{\Delta}{r^2}

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