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

Explanation

` L.H.S = (b-c)/a = (k sin B- k sin C)/(k sin A)`
` = (sin B - sin C)/(sinA) = (2cos.(B+C) /2 * sin . (B-C)/2 )/(2sin. A/2 * cos. A/2 )`
` = (cos. (B+C)/2* sin. (B-C)/2 )/(sin. (180^(@)- (B+C))/2 * cos .(180^(@)-(B+C))/2)`
` (cos. (B+C)/2 * sin. (B-C)/2 )/(sin. {90^(@)- (B+C)/2}* cos. { 90^(@) - (B+C)/2})`
` (cos (B+C)/2*sin.(B-C)/2 )/(cos. (B+C)/2 * sin. (B+C)/2 )= (sin(B/2-C/2))/(sin(B/2+C/2))`
` (sin. B/2 cos.C/2 - cos.B/2 sin.C/2)/(sin.B/2 cos.C/2 +cos.B/2 sin.C/2)`
` (tan. B/2 - tan.C/2)/(tan.B/2+tan.C/2)`
` ( cos. B/2 cos.C/2` से अंश और हर को भाग देने पर )
` = R.H.S`