& # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; defines the set a * b = {x ｜ x ∈ a, and X does not belong to B}. If a = {1.2.3.4.5}, B = {2.4.5}, then the number of subsets of a * B is?

A * b = {1,3}, so the number of subsets is 2 ^ n = 2 ^ 2 = 4

Senior one mathematics, please answer in detail, thank you! (16:11:58)
If the logarithm function y = ㏒ (A2-1) x is in the interval (0,1), its value is always positive, then the value range of real number a

Let the function be positive
X is in (0,1)
Then A2-1 should also be in (0,1)
So 0

Trigonometric function problem (3018:56:33)
Sin (2a + b) = 3sin B, a is not equal to K π + π / 2, a + B is not equal to K π + π / 2 (k belongs to Z), prove: Tan (a + b) = 2tan a (Note: A is AFA &# 160; &# 160; &# 160; B is Bida)

Here we need to use the skill of angle splitting, 2A + B = a + B + A, B = a + B-A;
Because sin (2a + b) = 3sin B
So sin [(a + b) + a] = 3sin [(a + b) - A]
The two sides are expanded: sin (a + b) * cosa + cos (a + b) * Sina = 3 * [sin (a + b) * cosa cos (a + b) * Sina]
The result is: 2Sin (a + b) * cosa = 2cos (a + b) * Sina
That is, Tan (a + b) = 2tan a

Trigonometric function (19:34:31)
If the angle X satisfies o

0=2√(2tanx*1/tanx)=2√2
Take the equal sign when 2tanx = 1 / TaNx
Obviously, TaNx has a positive solution
So we can get the equal sign
So the minimum value is 2 √ 2

Trigonometric function (2 21:19:26)
Let f (x) = cosx / cos (30-x), then f (1 °) + F (2 °) +. + F (59 °)=

f(1°)+f(2°)+.+f(59°)= [f(1°)+f(59°)]+[f(2°)+f(58°)] + ... + [f(29°)+f(31°)] + f(30°)
According to the sum difference product formula, cos α + cos β = 2cos [(α + β) / 2] · cos [(α - β) / 2]
And there is: cos γ = cos (- γ)
The results show that [f (1 °) + F (59 °)] = cos1 / cos (29) + cos59 / cos (- 29) = (cos1 + cos59) / cos29 = 2cos30 · cos29 / cos29 = 2cos30, similarly:)] + [f (2 °) + F (58 °)] =... = [f (29 °) + F (31 °)] = 2cos30, and f (30 °) = cos30,
The formula = 29.2cos30 ° + cos30 ° = 59.cos30 ° = (59 / 2) · √ 3

Trigonometric functions (27 19:11:23)
The minimum and maximum of y = SiNx + cosx + SiNx * cosx

Let t = SiNx + cosx t in the range [- √ 2, √ 2]
Then sinxcosx = (T ^ 2-1) / 2
So y = t + (T ^ 2-1) / 2
=[(t+1)^2-2]/2
(draw a picture by yourself, and you can see it easily.)
When t = - 1, the minimum value of y = - 1
When t = √ 2, the maximum value of y = (1 + 2 √ 2) / 2

Trigonometric function (19 11:18:54)
Find the maximum and minimum value of the function y = (1 + SiNx) (1 + cosx)

Y = 1 + SiNx + cosx + SiNx * cosx let SiNx + cosx = t, so the square of (SiNx + cosx) = the square of SiNx + the square of cosx + 2sinx * cosx = 1 + 2sinx * cosx = t, so SiNx * cosx = 1 / 2 * (the square of T - 1) so y = 1 + T + 1 /

How to prove that four points are coplanar

Method 1
Firstly, it is proved that three points determine a plane, and then the fourth point is in the plane
Method 2: we might as well set four points as a, B, C and D
It is proved that a, B and C determine a plane, then B, C and d also determine a plane, and finally the two planes coincide
And four points coplanar = two lines intersect or parallel

What is the minimum positive angle

The angle must be positive
What is the smallest?
We know that there are innumerable angles with the same terminal edge of an angle, but there is only one smallest one. The smallest one is when t is 0. For example, what is the smallest positive angle with the same terminal edge of 380 '?
20`,380`=1*360`+20`

From the fixed point a (6,8) to the circle: x2 + y2 = 16, any secant line intersects the circle at a and B, the trajectory equation of the midpoint P of the chord AB is obtained

The letter of the fixed point is not suitable. Change the letter to M
The center of the circle is o
OP vertical ab
Om midpoint n (3,4)
OA=10
So the distance from P to n = 5
So the trajectory of P is a circle, (x-3) ² + (y-4) ² = 25 (the part in a known circle)

& # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; & # 160; defines the set a * b = {x ｜ x ∈ a, and X does not belong to B}. If a = {1.2.3.4.5}, B = {2.4.5}, then the number of subsets of a * B is?