Question

\(\sin^2\dfrac{A}{2}+\sin^2\dfrac{B}{2}+\sin^2\dfrac{C}{2}\)\(=\sin\dfrac{A}{2}\sin\dfrac{B}{2}\sin\dfrac{C}{2}\)

Answer 1

Sai đề: \(sin^2\dfrac{A}{2}+sin^2\dfrac{B}{2}+sin^2\dfrac{C}{2}=1-2sin\dfrac{A}{2}.sin\dfrac{B}{2}.sin\dfrac{C}{2}\)

\(sin^2\dfrac{A}{2}+sin^2\dfrac{B}{2}+sin^2\dfrac{C}{2}\)

\(=1-\dfrac{cosA+cosB}{2}+sin^2\dfrac{C}{2}\)

\(=1-cos\dfrac{A+B}{2}.cos\dfrac{A-B}{2}+sin\dfrac{C}{2}.cos\dfrac{A+B}{2}\)

\(=1-sin\dfrac{C}{2}.cos\dfrac{A-B}{2}+sin\dfrac{C}{2}.cos\dfrac{A+B}{2}\)

\(=1+sin\dfrac{C}{2}\left(cos\dfrac{A+B}{2}-cos\dfrac{A-B}{2}\right)\)

\(=1-2sin\dfrac{A}{2}.sin\dfrac{B}{2}.sin\dfrac{C}{2}\)