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If A+B+C=180^(@), then the value of cot....

If `A+B+C=180^(@)`, then the value of `cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2)` will be

A

`2cot.(A)/(2)cot.(B)/(2)cot.(C)/(2)`

B

`4cot.(A)/(2)cot.(B)/(2)cot.(C)/(2)`

C

`cot.(A)/(2)cot.(B)/(2)cot.(C)/(2)`

D

`8cot.(A)/(2)cot.(B)/(2)cot.(C)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`A+B+C=180^(@)`
`therefore (A)/(2)+(B)/(2)=90^(@)-(C)/(2)`
`therefore cot((A)/(2)+(B)/(2))=cot(90^(@)-(C)/(2))`
or `(cot.(A)/(2).cot.(B)/(2)-1)/(cot.(B)/(2)+cot.(A)/(2))=tan.(C)/(2)=(1)/(cot.(C)/(2))`
or `(cot.(A)/(2)cot.(B)/(2)-1)cot.(C)/(2)=cot.(B)/(2)+cot.(A)/(2)`
`cot.(A)/(2).cot.(B)/(2).cot.(C)/(2)=cot.(C)/(2)+cot.(B)/(2)+cot.(A)/(2)`
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