51.0k views
16 votes
Show and/or explain that sin C = sin(A+B) in any & ABC.

1 Answer

2 votes


\text{In any triangle ABC,}~\\\\A +B+C = \pi\\\\\text{Now,}\\\\\text{L.H.S}\\\\=\sin C\\\\=\sin\left[\pi - (A+B) \right]\\\\=\sin(A+B)\\\\=\text{R.H.S}\\\\\text{Showed.}

User Gwyn Morfey
by
5.9k points