Given the function y = cos (x - π / 6) [√ 3sin (x - π / 6) + cos (x - π / 6)], X ∈ R, find the maximum value of function y and the set of corresponding independent variables X

Given the function y = cos (x - π / 6) [√ 3sin (x - π / 6) + cos (x - π / 6)], X ∈ R, find the maximum value of function y and the set of corresponding independent variables X

Y = cos (x - π / 6) [√ 3sin (x - π / 6) + cos (x - π / 6)] = 2cos (x - π / 6) [(√ 3 / 2) * sin (x - π / 6) + (1 / 2) * cos (X - π / 6)] (sine formula of sum of two angles) = 2cos (x - π / 6) * sin (x - π / 6 + π / 6) = 2cos (x - π / 6) SiNx (sum difference formula) = sin (x + X - π / 6) + sin

The maximum value of the function y = 3sin + root COS is
It should be y = 3sin pie x + root 7 cos pie X's maximum is

Y = 3sin pie x + radical cos pie x
=3-3 (radical cos faction x) ^ 2 + radical cos faction x
=-[radical 3cos pie X-1 / (2 radical 3)] ^ 2 + 3 + 1 / 12
=-[radical 3cos pie X-1 / (2 radical 3)] ^ 2 + 37 / 12
The maximum value of function y = 3sin + root COS is 37 / 12
The maximum value of y = 3sin pie x + root 7 cos pie x is 4

Find the maximum value of square * x + 3sin of function f (x) = 2 * cos on [- π / 2, π / 2]

The square * x of COS = the square * x of 1-sin, then f (x) = 2 * (the square * x of 1-sin) + 3sin = - 2sinx ^ 2 + 3sinx + 2, let SiNx be t, in [- π / 2, π / 2] there is t, in [- 1,1] solve the equation g (T) = - 2T ^ 2 + 3T + 2 = 0, then t is equal to - 1 / 2 or 2, then G (- 1) is the minimum value - 3, G (1) is the maximum value 3, so f (x) = 2 * C

On every curve of the image with inverse scale function y = 1-k / x, y increases with the increase of X
1. Find K
2. Under the condition of one, point a is hyperbola y = 1-k / X (x)

Let a (x, (1-k) / x), then B ((1-k) / x, (1-k) / x), from ab ^ 2-oa ^ 2 = 4, we get [x - (1-k) / x] ^ 2 - {x ^ 2 + [(1-k) / x] ^ 2} = 4, ■ - 2 (1-k) = 4, k = 3