Bài 1 :

1/ A=(1+sinx)tan² x(1-sinx)

2/ B=(1-sin² x)cot² x+1-cot² x

3/ C=(tanx+1/tanx)² - (tanx-1/tanx)²

Bài 2 :

1/ \(cos\alpha=\frac{1}{2}\) biết 0<\(\alpha< \frac{\pi}{2}\)

2/ sin\(\alpha=-\frac{2}{3}\) biết \(-\frac{\pi}{2}< \alpha< 0\)

3/ tan\(\alpha\) = \(-\sqrt{\frac{3}{3}}\) biết \(-\frac{\pi}{2}< \alpha< 0\)

4/ cot\(\alpha=-2\) biết \(\frac{3\pi}{2}< \alpha< 2\pi\)

Giúp mình với ạ mình cảm ơn .

Câu 3 : Giác các bất phương trình sau

a , \(\frac{2}{x-1}< \frac{5}{2x-1}\)

b , \(\frac{1}{x+1}< \frac{1}{\left(x-1\right)^2}\)

c , \(\frac{1}{x}+\frac{2}{x+4}< \frac{3}{x+3}\)

d , \(\frac{x^2-3x+1}{x^2-1}< 1\)

e , \(\frac{3}{2-x}< 1\)

f , \(\frac{x^2+x-3}{x^2-4}\ge1\)

g , \(\frac{1}{x-1}+\frac{1}{x+2}>\frac{1}{x-2}\)

h , \(\frac{3x-4}{x-2}>1\)

i , \(\frac{2x-5}{2-x}\ge-1\)

k , \(\frac{-4}{3x+1}< \frac{3}{2-x}\)

l , \(\frac{2}{x-3}+\frac{4}{x+3}\le\frac{5x-1}{x^2-9}\)

m , \(\frac{x+1}{18}+\frac{-2x+1}{9}\le1\)

Bài 1: Tìm tập nghiệm của phương trình và bất phương trình

a) \(\frac{x^2+2x+8}{|x+1|}< 0\)

b) \(\frac{2x^2-3x+1}{|4x-3|}< 0\)

c) \(|x^2-x-12|>x+12-x^2\)

d) \(|x^2-5x+6|=x^2-5x+6\)

e) \(\frac{|x^2-8x+12|}{\sqrt{5-x}}>\frac{x^2-8x+12}{\sqrt{5-x}}\)

f) \(\frac{|x^2-7x+10|}{\sqrt{x-3}}=\frac{x^2-7x+10}{\sqrt{x-3}}\)

g) \(\frac{1}{x-3}\ge\frac{1}{x+3}\)

h) \(\frac{2x^2-3x+4}{x^2+2}>1\)

Bài 2: Tìm tập xác định của hàm số

a) y =\(\sqrt{\frac{2}{x^2+5x+6}}\)

b) y = \(\sqrt{x^2+x+2}+\frac{1}{2x-3}\)

c) y = \(\sqrt{\frac{x^2-1}{1-x}}\)

\(\frac{a^3}{b^2}\)+\(\frac{b^3}{c^2}\)+\(\frac{c^3}{a^2}\) ≥ \(\frac{a^2}{b}\)+\(\frac{b^2}{c}\)+\(\frac{c^2}{a}\)(1)

(2) \(\frac{a^5}{b^3}\)+\(\frac{b^5}{c^3}\)+\(\frac{c^5}{a^3}\) ≥ \(a^2\)+\(b^2\)+\(c^2\)
chứng minh bằng cosi
giúp mk với :<<<<

Bài 1.

A=\(\frac{1}{1}\)x\(\frac{1}{2}\)x\(\frac{1}{2}\)x\(\frac{1}{3}\)x\(\frac{1}{3}\)x\(\frac{1}{4}\)x\(\frac{1}{4}\)x\(\frac{1}{5}\)x\(\frac{1}{5}\)x\(\frac{1}{6}\)

Bài 2.

B=\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+\(\frac{1}{3x4}\)+\(\frac{1}{4x5}\)+\(\frac{1}{5x6}\)

Bài 3.

B=\(\frac{2}{1x2}\)+\(\frac{2}{2x3}\)+\(\frac{2}{3x4}\)+\(\frac{2}{4x5}\)+\(\frac{2}{5x6}\)

Bài 4.

C=\(\frac{2}{1x3}\)+\(\frac{2}{3x5}\)+\(\frac{2}{5x7}\)+\(\frac{2}{7x9}\)+\(\frac{2}{9x11}\)

Bài 5.

C=\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)

Bài 6.Tính bằng cách thuận tiện nhất.

a.(792,81 x 025 + 792,81 x 0,75) x (11 x 9 - 900 x 0,1 - 9).

b.\(\frac{7,2:2x57,2+2,86x2x64}{4+4+8+12+20+....+220}\)

c.\(\frac{2003x14+1998+2001x2002}{2002+2002x503+504x2002}\)

d.\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{28}\)

đ.3,54 x 73 + 0,23 x 25 + 3,54 x 27 + 0,17 x 25

e.\(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)

g.\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)\)

Giải các bất phương trình sau:

a) \(\frac{x^2-9x+14}{x^2+9x+14}\ge0\)

b) \(\frac{x^2+1}{x^2+3x-10}< 0\)

c) \(\frac{10-x}{5+x^2}>\frac{1}{2}\)

d) \(\frac{x+1}{x-1}+2>\frac{x-1}{x}\)

e) \(\frac{1}{x+1}+\frac{2}{x+3}\le\frac{3}{x+2}\)

f) \(\frac{x-3}{x+1}-\frac{x-2}{x-1}\le\frac{x^2+4x+15}{x^2-1}\)

g) \(\frac{x^2-4x+3}{x^2-2x}\ge0\)

h) \(\frac{x+2}{3x+1}\le\frac{x-2}{2x-1}\)

i) \(\frac{11x^2-5x+6}{x^2+5x+6}\le x\)

j) \(\frac{\left(1-2x\right)\left(\sqrt{3}x+1\right)}{2\sqrt{2}x-1}\ge0\)

k) \(\frac{\left(5x+1\right)-\left(7x-2\right)}{\left(-x^2-1\right)\left(x^2-4x+4\right)}\le0\)

l) \(\frac{1}{x^2-7x+5}\ge\frac{1}{x^2+2x+5}\)

m) \(\frac{\left(x-1\right)\left(x^3-1\right)}{x^2+\left(1+2\sqrt{2}\right)x+2+\sqrt{2}}\le0\)

Giải bất phương trình chứa ẩn ở mẫu :

a. \(\frac{1}{x-2}\)\(\le\)\(\frac{1}{2x+1}\)

b. \(\frac{x^2+3x-1}{2-x}\)\(\ge\)0

c. \(\frac{x^2-3x+1}{x^2-1^{ }}\)<1

d. \(\frac{2}{x+4}\)+\(\frac{1}{x}\) <\(\frac{3}{x+3}\)