Cho tam giác ABC
CMR :$a = \frac{P.sin\frac{A}{2}}{cos\frac{B}{2}.cos\frac{C}{2}}$
thx mọi người
CMR :$a = \frac{P.sin\frac{A}{2}}{cos\frac{B}{2}.cos\frac{C}{2}}$
Started By wjzhweo, 21-03-2012 - 22:17
#1
Posted 21-03-2012 - 22:17
#2
Posted 24-03-2012 - 12:58
Giả thiết đã cho tương đương với $\frac{a}{P}=\frac{sin\frac{A}{2}}{cos\frac{B}{2}cos\frac{C}{2}}$
Theo định lí hàm số sin, ta có:
$\frac{a}{P}=2\frac{2RsinA}{a+b+c}=\frac{4RsinA}{2R(sinA+sinB+sinC)}=\frac{8Rsin\frac{A}{2}cos\frac{A}{2}}{8Rcos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}}=\frac{sin\frac{A}{2}}{cos\frac{B}{2}cos\frac{C}{2}}$ $\Rightarrow Q.E.D$
Theo định lí hàm số sin, ta có:
$\frac{a}{P}=2\frac{2RsinA}{a+b+c}=\frac{4RsinA}{2R(sinA+sinB+sinC)}=\frac{8Rsin\frac{A}{2}cos\frac{A}{2}}{8Rcos\frac{A}{2}cos\frac{B}{2}cos\frac{C}{2}}=\frac{sin\frac{A}{2}}{cos\frac{B}{2}cos\frac{C}{2}}$ $\Rightarrow Q.E.D$
Edited by moonlight0610, 24-03-2012 - 17:36.
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