Tìm kiếm
Nam
CMR: $\Delta ABC$ đều nếu thỏa mãn điều kiện sau:
1) $\sqrt{tan A}+\sqrt{tan B}+\sqrt{tan C}=\sqrt{cot \frac{A}{2}}+\sqrt{cot \frac{B}{2}}+\sqrt{cot \frac{C}{2}}$
2) $tan^6\frac{A}{2}+tan^6\frac{B}{2}+tan^6\frac{C}{2}=\frac{1}{9}$
3) $cos A+cos B+cos C=sin \frac{A}{2}+sin\frac{B}{2}+sin\frac{C}{2}$
4) $\left\{\begin{matrix} sinB+sinC=2sinA\\ tanB+tanC=2sinA \end{matrix}\right.$
5) $\frac{1}{sin^22A}+\frac{1}{sin^22B}+\frac{1}{sin^22C}=\frac{1}{2cosA.cosB.cosC}$
6) $\frac{a}{m_{a}}=\frac{b}{m_{b}}=\frac{c}{m_{c}}$
7) $P+R=(2+3\sqrt{3})r$
Đã update ^^
