Given Tana = 1, then the value of (2sina COSA) / (2sina + COSA)

tanA=sinA/cosA=1
So Sina = cosa
So (2sina COSA) / (2sina + COSA)
=（2sinA-sinA)/(2sinA+sinA)
=sinA/(3sinA)
=1/3

When 20 matchsticks are placed on each side to form a triangle, how many matchsticks are needed
A series of triangle patterns made of matchsticks are placed in this way. When the actual number of matchsticks is placed on each side, the total number of matchsticks is 3; when the actual number of matchsticks is placed on each side, the total number of matchsticks is 9; when the number of matchsticks is 3, the total number of matchsticks is 18; when the number of matchsticks is 20, the total number of matchsticks is 9; when the number of matchsticks is n, the total number of matchsticks is 18, What is the total number of matchsticks needed
When there are four matchsticks on each side, the total number of matchsticks needed is 30
When 5 matches are placed on each side, the total number of matches needed is 45

There are n triangles in the row of the nth root on each side, so there are 1 + 2 + 3 + 4 + +There are n triangles, and each triangle is made up of three matches, so there are (1 + 2 + 3 + 4 +...) +N) * 3 is 3 * n * (n + 1) / 2 matches
When there are 20 matchsticks on each side, the total number of matchsticks needed is 630

Use the matchstick to build the figure in the way shown in the figure. Build it in this way and build the nth one
Picture:
Number of matchsticks: 12. 18。 twenty-four

According to the analysis of the title meaning, the first figure uses 12 matches; that is, 12 = 6 (1 + 1); the second figure uses 18 matches; that is, 18 = 6 (2 + 1); the second figure uses 18 matches;
The third figure uses 24 matches; that is, 24 = 6 (3 + 1);
… In this way, it takes 6N + 6 matches to build the nth figure

How many matchsticks do you need to make the nth figure?
Serial number
1 2 3 4 ……
4 7 10 13 ……

3n+1

Use a matchstick to make the following patterns: ① 5 patterns, ② 8 patterns, ③ 12 patterns
(1) How many matchsticks does the nth figure need?
(2) Can the number of matchsticks be 70 or 63?

(1) . n is odd 1 / 2 (7n + 3)
N is even 1 / 2 (7n + 2)
(2) . no, because according to the above formula, X is not an integer

Place a trapezoid and add a trapezoid every time
1> 5 (pieces)
2>.8
3>.12
4>.15
5>.19
...
How many matchsticks are used in the nth figure?

If n is odd, 5 + 7 * (n-1) / 2
N is even number, match is 1 + 7 * n / 2

How many matchsticks does the nth figure have?
The first figure is 4
The second figure has 7 roots
The third figure is 10
The fourth figure has 13 roots
The fifth figure is 16
The sixth figure is 19
How many matchsticks does the nth figure need?

The first one is 1 + 3
The second one is 1 + 3 * 2
The third is 1 + 3 * 3
And so on, the nth needs 1 + 3N roots

As shown in Figure 12, three matchsticks are assembled into three squares. How to move x matchsticks into a centrosymmetric figure? What is the minimum value of X

The dotted line moves to the red line, x = 2

12 matches make 4 small squares. Move 3 matchsticks to make 4 small squares become 3 small squares

Move the two matches of the small square border in the upper right corner of Tian character to the left side of the border in the lower left corner, and then move the small square on the left side of the horizontal line at the bottom of Tian character to the left to form a pin shape~
one
▕▔｜▔▏2 1 ▕▔▏
— — —→ ＿ ▔ ＿
▕＿｜＿▏ 2▕＿▏ ▕＿▏
3 3

Given Tana = 1, then the value of (2sina COSA) / (2sina + COSA)