1.

किसी `Delta ABC` में सिद्ध कीजिए कि- `asin((B-C)/(2))=(b-c)cos.(A)/(2)`

Answer» sine सूत्र से , `(sinA)/(a)=(sinB)/(b)=(sinC)/(c)=(1)/(k)` (माना)
`a=k sin A`
`b=k sinB`
`c=k sin C`
इसलिए `(b-c)/(a)=(k sin B-ksinC)/(k sin A)`
`=(sinB-sinC)/(sinA)`
`=(2cos ((B+C)/(2))sin((B-C)/(2)))/(2sin.(A)/(2)cos.(A)/(2))=(cos((pi)/(2)-(A)/(2))sin((B-C)/(2)))/(sin.(A)/(2)cos.(A)/(2))`
`=(sin.(A)/(2)sin((B-C)/(2)))/(sin.(A)/(2)cos.(A)/(2))=sin((B-C)/(2))/(cos.(A)/(2))`
इसलिए `a sin((B-C)/(2))=(b-c)cos.(A)/(2)`.


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