किसी त्रिभुज ABC में सिद्ध कीजिए - `(sin A)/(a)=(sin B + sin C)/(b + c)=(sin B - sin C)/(b-c)`.

Explanation

साइन सूत्र से, `(sin A)/(a)=(sin B)/(b)=(sin C)/(c )=k`, (माना) |
तब `(sin A)/(a)= k rArr sin A = ak`
`rArr (sin B + sin C)/(b + c)=(bk+ck)/(b+c)=(k(b+c))/(b+c)=k`
`rArr (sin B - sin C)/(b-c)=(bk-ck)/(b-c)=(k(b-c))/(b-c)=k`
अतः, `(sin A)/(a)=(sin B + sin C)/(b+c)=(sin B-sin C)/(b-c)=k " "` इति सिद्धम्