If the moving line x = a intersects with the function f (x) = √ 3sin (x + π / 6) and G (x) = cos (π / 3-x) at two points m and N respectively, then the maximum value of | Mn | is

If the moving line x = a intersects with the function f (x) = √ 3sin (x + π / 6) and G (x) = cos (π / 3-x) at two points m and N respectively, then the maximum value of | Mn | is

g(x)=cos(π/3-x)=sin(x+π/6),
The maximum value of | Mn | is √ 3-1

If the moving line x = a intersects the image of F (x) = sin (x + π 6) + sin (x - π 6) and G (x) = cosx at M and N points respectively, then the maximum value of | Mn | is______ ．

The function f (x) = sin (x + π 6) + sin (x - π 6) = sinxcos π 6 + cosxsin π 6 + sinxcos π 6-cosxsin π 6 = 3sinx. Let m (x0, 3sinx0), n (x0, cosx0), then | Mn | = | 3sinx0-cosx0 | = | 2Sin (x0 - π 6) | ≤ 2, if and only if x0 - π 6 = k π + π 2, K ∈ Z

Factorization of a ^ 3 + B ^ 3 + C ^ 3 + BC (B + C) + AC (a + C) + AB (a + b)

a^3+b^3+c^3+bc(b+c)+ac(a+c)+ab(a+b)
=(a^3+a^2b+a^2c)+(b^3+b^2c+ab^2)+(c^3+bc^2+ac^2)
=a^2(a+b+c)+b^2(a+b+c)+c^2(a+b+c)
=(a+b+c)(a^2+b^2+c^2)