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

Explanation

` R.H.S = (c+a)/(a+b) * cos. C/2 * cos. (A-B)/2 `
` = ( k sin C + k sin A ) / ( k sin A + k sin B) * cos . C/A cos. (A-B)/2`
` = (sin C + sinA)/(sinA + sinB) * cos. C/2 cos. (A-B)/2`
= ` (2 sin. (C+A)/2 * cos. (C-A)/2)/(2sin.(A+B)/2* cos.(A-B)/2 )*cos.C/2 *cos.(A-B)/2`
` (sin. (180^(@)-B)/2*cos.((180^(@)-(A+B)-A)/2))/(sin. (180^(@)-C)/2) * cos. C/2`
` (sin(90^(@) - B/2)cos{90^(@)- (A+B/2)})/(sin(9^(@)-C/2))* cos.C/2`
` = (cos. B/2 * sin ( A + B/2)) /(cos.C/2 )*cos.C/2 `
` = cos. B/2 * sin (A+B/2) = L.H.S.`