It is known that in △ ABC, ∠ ABC is an acute angle, and ∠ ABC = 2 ∠ ACB, ad is the height on the edge of BC, extend AB to e, make be = BD, connect ed and extend AC to F. verification: AF = CF = DF

It is known that in △ ABC, ∠ ABC is an acute angle, and ∠ ABC = 2 ∠ ACB, ad is the height on the edge of BC, extend AB to e, make be = BD, connect ed and extend AC to F. verification: AF = CF = DF

It is proved that: as shown in the figure, ∵ be = BD, ∵ 1 = ∠ e, ∵ ABC = 1 +} e = 2} 1, ∵ ABC = 2} ACB, ∵ 1 =} ACB, and ∵ 1 =} 2, ∵ 2 =} ACB, ∵ CF = DF, ∵ ad is the height on the edge of BC, ∵ 2 +} 3 = 90 degree, ? ACB +} 4 = 90 degree, ∵ 3 =} 4, ? AF = DF, AF = CF = DF

a. If B is any real number and the maximum of | a + B |, | A-B |, | B-1 | is m, then ()
A. M≥0B. 0≤M≤12C. M≥1D. M≥12

Trigonometric calculus y = (1 + tan2x) / (1-tan2x) for dy / DX
For y = (1 + tan2x) / (1-tan2x), find dy / DX

y＝(1+tan2x)/(1-tan2x)
→y＝tan(2x+π/4).
∴y'＝sec^2(2x+π/4)·(2x+π/4)'
∴dy/dx＝2[sec(2x+π/4)]^2.

If we know that the odd function f (x) is a monotone decreasing function on [- 1,0], and α and β are two inner angles of an acute triangle and α > β, then the following conclusion is correct ()
A. f（cos α）＞f（cos β）B. f（sin α）＞f（sin β）C. f（sin α）＞f（cos β）D. f（sin α）＜f（cos β）

∵ odd function y = f (x) is a monotone decreasing function on [- 1,0]; f (x) is a monotone decreasing function on [0,1]; f (x) is a monotone decreasing function on [- 1,1]; and α and β are the two inner angles of an acute triangle ∵ α + β > π 2 ∵ α > π 2 - β ∵ sin α > sin (π 2 - β) = cos β > 0 ∵ f (sin α) < f (COS β). Therefore, D

The range of function f (x) = LG (x ^ 2-2x + 11) is

x^2-2x+11=（x+1)^2+10>0
Minimum = 10
The value range of is: [1, + infinity)

Finding the derivative of function y = e ^ cosx

Y=e^cosx
Y'=e^cosx*(cosx)'
=-sinxe^cosx

Oral problems, application problems, the more the better, urgent, the best

Summary of junior high school mathematics application problems. Key points and common types of problems. The ability of solving application problems by equations (groups) is tested. The key point is to solve application problems by quadratic equations or fractional equations. The exercises are mainly about engineering problems and itinerary problems. Some economic problems have appeared in recent years

General solution of differential equation (x ^ 2 + 1) y '+ 2XY cosx = 0

This is actually a total differential equation
It is equivalent to D ((X & sup2; + 1) y - SiNx) = 0
The solution is (X & sup2; + 1) y - SiNx = C
See resources for details

This is a general formula of 8, 24, 48, 80. Do you have any general method to solve this kind of series,
Because this kind of sequence is neither equal difference nor equal ratio, it often makes me turn around and find a good method to solve this kind of problem

A sequence divided by 8
1 3 6 10……
1+2=3
3+3=6
6+4=10
Item n + (n + 1) = item (n + 1)

() × () = () () () () fill in the box with nine numbers 123456789 to make the equation true. Each number can not be used repeatedly

1738 * 4 = 6952
1963 * 4 = 7852