It is proved by unit circle that the sum of sine absolute value and cosine absolute value of angle α is not greater than root 2 fast

It is proved by unit circle that the sum of sine absolute value and cosine absolute value of angle α is not greater than root 2 fast

Make a unit circle and connect a diameter ab. take the diameter as one side and a as the vertex to make an angle α. Connect the other side with the intersection C of the circle and B. triangle ABC is a right triangle, so sin α = BC / AB, cos α = AC / ab. so the sum of sine absolute value and cosine absolute value is (AC + BC) / AB, because when AC + BC is the maximum, that is triangle

Analytic geometry proves that the sum of sine absolute value and cosine absolute value of angle α is not greater than root 2

Sin α + cos α = radical 2 * sin (π / 4 + α)=

If the absolute value of X is less than or equal to π / 4, what is the value of SiNx

-2 / 2 root less than or equal to SiNx less than or equal to 2 / 2 root 2
Please accept this answer

Calculation: - 2m (m ^ 2-1 / 2m + 3)

-2m(m^2-1/2m+3)
=(-2m)*m^2-(-2m)*1/2m+(-2m)*3
=-2m^3+m^2-6m

What is 19991999 * 19991998-19992000 * 19991997

=399680004024002-399680004024000
=2

199919982199919972+199919992−2

Let 19991998 = x, then the original formula = X2 (x − 1) 2 + (x + 1) 2 − 2 = 12

199919982199919972+199919992−2

Let 19991998 = x, then the original formula = X2 (x − 1) 2 + (x + 1) 2 − 2 = 12

Square of 19991998 / (square of 19991997 + square of 19991999-2)
/Denotes a division sign

Replace 19991997 with 19991998-1
Replace 19991999 with 19991998 + 1
After substituting, it's OK. Is it 0.5

19991999*19991998—19992000*19991997

19991999*19991998—19992000*19991997
=19991999*19991997+19991999—19992000*19991997
=19991999+（19991999—19992000）*19991997
=19991999-19991997
=2

If M-1 / 2 ＜ x ≤ m + 1 / 2 (where m is an integer), then M is called the integer nearest to the real number X. it is denoted as {x}, that is {x} = M. on this basis, the following proposition about the function f (x) = {x} - x is given, then the true proposition is
1. The function f (x) is an increasing function on [- 1 / 2,1 / 2],
2. The image of the function y = f (x) is symmetric with respect to the line x = K / 2 (k is an integer)

1) , 2), 3) correct
The definition is given if M-1 / 2