Induction formula of trigonometric ratio of the same angle Ask a question to simplify [sin (a - π) * CTG (A-2 π)] / cos (a - π) * Tan (A-2 π)]

Induction formula of trigonometric ratio of the same angle Ask a question to simplify [sin (a - π) * CTG (A-2 π)] / cos (a - π) * Tan (A-2 π)]

sin(a-π）＝-sin(π-a）=-sina
cot（a-2π）=cota
sin(a-π）＝cos(π-a）=-cosa
tan（a-2π）=tana

Mathematical induction formula
Cos (π / 6 - α) = 1 / 3
Finding cos (5 π / 6 + α)
Sin（2π/3-α）

-1/3
and 1/3

Mathematics problems of senior one, induction formula
It is known that f (cosx) = cos17x
Verification: F (SiNx) = sin17x

It is proved that f (cosx) = cos17x. Let x = (π / 2) - T. = = = > cosx = cos [(π / 2) - t]= sint.cos17x=cos So f (cosx) = f [cos (π / 2-T)] = cos [8 π + (π / 2) - 17T] = cos [(π / 2) - 17T] = sin17t. F (SiNx) = sin17x

High school mathematics - what is the formula for calculating parallelogram with vector?
If the vectors on both sides are a and B, respectively
The formula I remember is under the root

Triangle AOE is congruent with COF, AE = CF, because ad = BC, BF = De, area of triangle AOE = 0.5ae × height of triangle AOE = 0.5ae × 0.5, area of triangle AOE is one twelfth of parallelogram, which is one sixth of triangle ACD

1. What is the solution set of inequality (3 - | x |) / (| x | - 2) ≥ 1 / 2?
2. What is the solution set of inequality (1 - | x | (x + 1) > 0?
3. If the solution set of inequality | x-a | > x is r, what is the value range of real number a?
4. What is the solution set of inequality | x ^ 2-9 | ≤ | x + 3 |?

1. The inequality is reduced to (3|x | - 8) / [2 (|x | - 2)] ≤ 0,
20, get - 1

Find the minimum value of y = (x ^ 2 + 13) / root sign (x ^ 2 + 4) and y = (x ^ 2 + 5) / root sign (x ^ 2 + 4)

Y = (x ^ 2 + 13) / root sign (x ^ 2 + 4) = y = (x ^ 2 + 4 + 9) / root sign (x ^ 2 + 4) = root sign (x ^ 2 + 4) + 9 / root sign (x ^ 2 + 4) > = 2 root sign (9) = 6. If and only if root sign (x ^ 2 + 4) = 9 / root sign (x ^ 2 + 4), that is, when x = + - root sign 5, y has a minimum value of 6. 2) let t = root sign (x ^ 2 + 4) > = 2 out of x = root sign (T ^ 2-4

High school mathematics -- basic inequality
We know that x + y + Z = 1
（1）x^2+y^2+z^2≥1/3
（2）x^（1/2）+y^（1/2）+z^（1/2）≤3^（1/2）
sorry,
Second floor, can you explain how x ^ 2 + y ^ 2 + Z ^ 2 + 2XY + 2XZ + 2yz = 1 comes from?

X + y + Z = 1 has x ^ 2 + y ^ 2 + Z ^ 2 + 2XY + 2XZ + 2yz = 1 and 2XY ≤ x ^ 2 + y ^ 2 2yz ≤ y ^ 2 + Z ^ 2 2zx ≤ Z ^ 2 + x ^ 2, so there are 3 (x ^ 2 + y ^ 2 + Z ^ 2) ≥ 1, all x ^ 2 + y ^ 2 + Z ^ 2 ≥ 1 / 3 have [x ^ (1 / 2) + y ^ (1 / 2) + Z ^ (1 / 2)] ^ 2 = x + y + Z + 2 (XY) ^ (1 / 2) + 2 (YZ 2 (XZ) ^ (1 / 2) ^ (1 / 2)

High school mathematics basic inequality urgent!
Given x ≥ 2 / 5, what is the minimum value of F (x) = x ^ 2-4x + 5 / 2X-4
Given A. B, C ∈ R, a + B + C = 1, prove 1 / A + 1 / B + 1 / C ≥ 9
Finding the minimum value of function x ^ 2 + 8 / X-1 (x > 1)

(1) f (x) = (x ^ 2-4x + 5) / (2X-4) = ((X-2) ^ 2 + 1) / (2 (X-2)) = (X-2) / 2 + 1 / (2 (X-2)) when (X-2) / 2 = 1 / (2 (X-2)), there is a minimum value, that is, when x = 3, there is a minimum value = 2 * √ ((X-2) / 2 * 1 / (2 (X-2))) = 2 * 1 / 2 = 1
⑵ 1/a+1/b+1/c
=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c
=1+(b+c)/a+1(a+c)/b+1(a+b)/c
=3+b/c+c/b+a/c+c/a+a/b+b/a
>=3+2+2+2
=9

For the manufacture of π 2m3 uncovered cylindrical barrel, the price for making the bottom metal plate is 30 yuan / m2, and the price for making the side metal plate is 20 yuan / m2=______ , high H=______ ．

If the material cost is s, then s = 30 π R2 + 40 π r = 30 π R2 + 20 π r = 30 π R2 + 10 π R + 10 π R ≥ 30 π 33 (yuan) if and only if 30 π R2 = 10 π R, that is, r = 393, then H = 392, so the answer is: 393m, 392m

What is the specific method of memorizing English words introduced by Mr. Yu Minhong?

First, memorizing words should be related to reading. Second, the difficulty of reading the words in an article should be close to the amount of words you have. If nearly half of the articles with two or three hundred words are new words, reading is not fun at all, There's no need. Recite the words in the passage you come across. To read and understand, there is another thing that takes almost the same amount of time as reciting the words, that is, to interpret the sentence structure. If you don't have the ability to interpret the sentence structure, it's useless to recite the words
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