chứng minh toán 10

E

eye_smile

Ta có: $cosA+cosB+cosC \le \dfrac{3}{2}$

\Leftrightarrow $2cos^2 \dfrac{A}{2}+2cos^2 \dfrac{B}{2}+2cos^2 \dfrac{C}{2}-3 \le \dfrac{3}{2}$

\Leftrightarrow $cos^2 \dfrac{A}{2}+cos^2 \dfrac{B}{2}+ cos^2 \dfrac{C}{2} \le \dfrac{9}{4}$

Lại có $(cos\dfrac{A}{2}+cos\dfrac{B}{2}+cos\dfrac{C}{2})^2 \le 3(cos^2 \dfrac{A}{2}+cos^2 \dfrac{B}{2}+ cos^2 \dfrac{C}{2})=\dfrac{27}{4}$

\Rightarrow đpcm.
 
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