Show that cot ""(A)/(2) + cot "" ...

Show that
` cot ""(A)/(2) + cot "" ( B)/(2) + cot "" ( C ) /(2) = (S^(2))/( Delta ) `

Text Solution

Verified by Experts

The correct Answer is:

`(s^2)/( Delta )`

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Show that r r_1 cot "" (A)/(2) = Delta .

Show that r_1 r_2 r_3 = r^3 cot^(2) "" (A)/(2) cot^(2) "" (B)/(2) cot^(2) "" ( C)/(2) .

Knowledge Check

r ( cot "" ( B) /(2) + cot "" ( C) /(2)) =

A

`a `

B

`b `

C

` c `

D

` 0`

r^(2) cot ""(A)/(2) cot ""(B)/(2) cot ""(C)/(2)

A

` Delta `

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C

` 3 Dela `

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` 4 Delta `

In Delta ABC, cot ""(A)/(2) +cot""(B)/(2) + cot""(C)/(2)=

A

`sin""(A)/(2)*sin""(B)/(2)""sin""(C)/(2)`

B

`cos""(A)/(2)*cos""(B)/(2)""cos""(C)/(2)`

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`tan""(A)/(2)*tan""(B)/(2)""tan""(C)/(2)`

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`cot""(A)/(2)*cot""(B)/(2)""cot""(C)/(2)`

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