`Delta ABC` में सिद्ध कीजिए कि -
` ( a+ b + c) ( tan . A/2 + tan . C/2 ) = 2b cot. B/2 `

Explanation

` L.H.S = ( a= b+c) (tan.A/2 + tan. C/2)`
` = 2s. [ sqrt(((s-b)(s-c))/(s(s-a)))+ sqrt(((s-a)(s-b))/(s(s-c)))`
` = 2s. sqrt((s-b)/s )[ sqrt(((s-c))/(s-a) )+ sqrt((s-a)/(s-c)]]`
` 2sqrt(s(s-b)) [ (s-c+s-a)/sqrt((s-a)(s-c))]`
` = 2 sqrt((s(a-b))/((s-a)(s-c)))(2s-a-c)`
` = 2 cot . B/2 * ( a+ b + c - a - c ) `
` = 2 cot. B/2 * (a+b+c-a-c)`
` = 2b cot. B/2 = R.H.S`