quanrrom97

1) $cos2x+sin2x=\sqrt{3}cos3x$

2) $sin(4x+140^{\circ})=cot(2x-110^{\circ})$

cm rằng với 3 số thực dương a,b,c sao cho abc=1 thi

    $\frac{1}{2+\frac{1}{a}}+\frac{1}{2+\frac{1}{b}}+\frac{1}{2+\frac{1}{c}}\leq 1$

tính A=tg20.tg80+tg80.tg140+tg140.tg20

$(a\sqrt{b+c}+b\sqrt{a+c}+c\sqrt{a+b})^{2}\leq (a+b+c)(2ab+2bc+2ac)$

cho các số dương a,b,x,y,z. Cmr:
1) $(\sqrt{a}+\sqrt{b})^{8}\geq 64ab(a+b)^{2}$
2) $\sqrt[3]{a}+\sqrt[3]{b}\geq 2^{8}ab(a+b)$
3) $(\frac{x}{y}+\frac{y}{x})^{32}\geq 8^{9}(\frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}})^{4}(\frac{x^{4}}{y^{4}}+\frac{y^{4}}{x^{4}})$
4) $(\frac{x}{y}+\frac{y}{x})^{70}\geq 16^{16}(\frac{x^{3}}{y^{3}}+\frac{y^{3}}{x^{3}})^{5}(\frac{x^{5}}{y^{5}}+\frac{y^{5}}{x^{5}})$