किसी `Delta ABC ` में सिध्द कीजिये :
`cot .(A)/(2) + cot .(B)/(2) + cot .(C )/(2)= cot .(A)/(2) cot. (B)/(2) cot .(C )/(2)`

Explanation

`A + B + C = 180^(@)`
`(A)/(2)+(B)/(2) = 90^(@) -(C )/(2)`
` :. , tan ((A)/(2)+(B)/(2)) = tan (90^(@) -(C )/(2))`
या `(tan .(A)/(2)+ tan .(B)/(2))/(1- tan .(A)/(2) tan. (B)/(2))= cot .(C )/(2)`
` = (1)/(tan .(C )/(2)) `
या `tan.(A)/(2) tan.(C )/(2) + tan .(B)/(2) tan .(C)/(2) = 1- tan. (A)/(2) tan.(B)/(2)`
या ` tan .(A)/(2) tan .(B)/(2) + tan.(B)/(2) tan.(C )/(2) + tan .(B)/(2) tan. (C)/(2) =1`
दोनो पक्षेां को `tan. (A)/(2) tan. (B)/(2) tan. (C)/(2) ` से भाग देने पर
cot `(C )/(2) + cot .(B)/(2) + cot .(A)/(2) = cot .(A)/(2) cot .(B)/(2) cot .(C )/(2)`
या `cot .(A)/(2) + cot .(B)/(2) + cot .(C )/(2) = cot .(A)/(2) cot .(B)/(2) cot .(C)/(2)`