Mathematics, 21.06.2021 01:50 jholland03
Cho alpha+ beta+ gamma = pi. Chứng minh A) sin alpha + sin beta + sin gamma = 4cos alpha/2*cos beta/2*cos gamma /2
Answers: 3
![=sin\alpha + sin\beta +sin\gamma\\\\=2 sin \frac{\alpha +\beta }{2} cos\frac{\alpha -\beta }{2} + sin\gamma\\\\=2 sin\frac{180-\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}cos \frac{\alpha - \beta}{2}+2 sin\frac{\gamma}{2}cos\frac{\gamma}{2}\\\\=2 cos\frac{\gamma}{2}\left [ cos \frac{\alpha - \beta}{2}+sin\frac{180-\alpha-\beta}{2}\\ \right ]\\\\=2 cos\frac{\gamma}{2}\times 2 cos\frac{\alpha}{2}cos\frac{\beta}{2}\\](/tpl/images/1380/0083/8b5b6.png)
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Cho alpha+ beta+ gamma = pi. Chứng minh A) sin alpha + sin beta + sin gamma = 4cos alpha/2*cos beta/...
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