加法公式的一个推导

Output

$AB\ast AC\ast sin(\alpha +\beta )=BD\ast AD+CD\ast AD$

$\because BD=AB\ast sin\alpha$ $CD=AC\ast sin\beta$ $\because AD=AB\ast cos\alpha =AC\ast cos\beta$

$AB\ast AC\ast sin(\alpha +\beta )=AB\ast sin\alpha \ast AC\ast cos\beta +AC\ast sin\beta \ast AB\ast cos\alpha$

$\therefore sin(\alpha +\beta )=sin\alpha cos\beta +cos\alpha sin\beta$

关联

正弦定理