Trigonometric function··· cos(π/5 +x) = -1/2 , How to simplify?

Trigonometric function··· cos(π/5 +x) = -1/2 , How to simplify?

Cos (π / 5 + x) = - 1 / 2, then π / 5 + x = 2K π + 2 π / 3 or π / 5 + x = 2K π - 2 π / 3, the solution is x = 2K π + 7 π / 15 or x = 2K π - 13 π / 15, where k is an integer
Fill in a number in each box below, the following equation holds, and the three denominators are prime to each other
1/□□+1/18=1/□□.
1/□□+1/21=1/□□.
First question
1/□□+1/18=1/□□.
Let the preceding denominator be a and the following denominator be B
The above formula can be written as 1 / A + 1 / 18 = 1 / B, 18b + A * b = 18a
According to the meaning of the title, a and B are integers greater than or equal to 10 and less than or equal to 99, and B is less than a, that is, 10 ≤ B < a ≤ 99
B cannot be greater than 18 (because 18B + A * b = 18a, if B is greater than 18, then a is negative)
In 10-18, only 11, 13, 17 and 18 are prime numbers. If B = 11, 13 and 17 are substituted into 18B + A * b = 18a to solve the equation, there is no integer solution after the first two numbers are substituted. If 17 is substituted into a = 306, there is no solution
If the denominator is required to be reciprocal, these two problems seem to have no solution
Trigonometric function
In the sharp triangle ABC, the opposite sides of the angle are a, B, C. the known vectors M = (2b-c, COSC), n = (a, COSA), and M is parallel to n
Find the size of angle A
If f (b) = root 3sinb CoSb, P, find the value range of F (b)
The opposite sides of angles a, B and C are a, B and C respectively
F (b) = root 3sinb + CoSb,
Angle a is 60 degrees and f (b) is between zero and half root six
I can't understand your question. There is no difference in length and angle
If there are n (n ∈ n +) elements in the set a, then the subset of a has____ True subset has___ The nonempty subsets have____ One
^What is it?
This involves permutations and combinations
For example, a = {1,4,5,7,8}
Then the subset takes their combination number,
That's C
Answer: subset 2 ^ n
Proper subset 2 ^ (n-1)
Nonempty subset 2 ^ (n-1)
Nonempty proper subset 2 ^ (n-2)
In the following formula, all denominators are four digits. Please fill in a number in each square to make the equation true
1/□□□□+1/2004=1/□□□‍ □
1 / 2004 + 1 / 2004 = 1 / 1002, I think it's this
The number of nonempty proper subsets of set {a, B, C, D} ()
A. 16 B. 15 C. 14 d. 13
∵ the set {a, B, C, D} has four elements, then the set {a, B, C, D} has 24 = 16 subsets, so the number of nonempty proper subsets of the set {a, B, C, D} is 14; so C
() * () * () = () + () + (), fill in the same integer in brackets to make the equation hold. Who knows what to fill in?
Let the integer be x, then x ^ 3 = 3x
If x = 0, the equation holds; if x is not zero, the original equation can be changed to
If x ^ 2 = 3, then x = positive and negative root three
Only x = 0
In fact, x ^ 3 = 3x, solve x = 0 or x = positive and negative root sign 3 (not integer, round off)
So x = 0
It can only be 0
Given the set a = {1,2,3,4,5,6}, find: (1) the number of subsets of a; (2) the number of nonempty proper subsets of a; (3) the number of nonempty subsets of A
(1) 6c2 + 6c1 + 6c3 + 6C4 + 6c5 + 6c6 + 1 = 64 and an empty set is added at the end
(2) 64-1-6c6 = 62 is an empty set and the same set
(3)64-1=63
=Have you studied permutation and combination?
Subsets can be
empty set
It contains 1 element and 6 elements
It contains 2 elements and 5 elements
It contains three elements and four
It contains 4 elements and 3 elements
It contains 5 elements and 2 elements
There are six elements, one in itself
Total 1 + 1 + 2 + 3 + 4 + 5 + 6 = 22 subsets
The nonempty proper subset is to remove itself and empty set 22-2 = 20
Nonempty subset is to remove the empty set and keep its own subset 22-1 = 21... Expansion
Subsets can be
empty set
It contains 1 element and 6 elements
It contains 2 elements and 5 elements
It contains three elements and four
It contains 4 elements and 3 elements
It contains 5 elements and 2 elements
There are six elements, one in itself
Total 1 + 1 + 2 + 3 + 4 + 5 + 6 = 22 subsets
The nonempty proper subset is to remove itself and empty set 22-2 = 20
Nonempty subset is to remove the empty set and keep its own subset 22-1 = 21
Isn't the number of subsets 65
1.7 2.6 3.6 question: different from the answer, I just don't know the way of thinking
Fill in the blanks with proper integers so that the equation () / 5 * 1 / 3 = 77 / () holds. How many groups of integers meet the conditions
(x)/5*1/3=77/(y)
xy=77*5*3=3*5*7*11
x=1,3,5,7,11,3*5,3*7,3*11,5*7,5*11,7*11,3*5*7,3*5*11,3*7*11,5*7*11,3*5*7*11
There are 15 groups in total
Negative numbers are not included!
Including negative 30 groups
What is the number of sets satisfying {a, B} proper subsets in a and containing {a, B, C, D, e}?
There are eight: {a, B}, {a, B, C}, {a, B, D}, {a, B, e}, {a, B, C, D}, {a, B, C, e}, {a, B, D, e}, {a, B, C, D, e}