F (x) = sin square x + 2 radical 3 sin (x + π / 4) cos (x - π / 4) - cos square X - radical 3 (1) Find the minimum positive period and monotone decreasing interval of function f (x) (2) Find the maximum and minimum values of function f (x) on [- π / 12,25 π / 36], and point out the corresponding value of X

F (x) = sin square x + 2 radical 3 sin (x + π / 4) cos (x - π / 4) - cos square X - radical 3 (1) Find the minimum positive period and monotone decreasing interval of function f (x) (2) Find the maximum and minimum values of function f (x) on [- π / 12,25 π / 36], and point out the corresponding value of X

The premise is: SiNx * SiNx + cosx * cosx = 1cos2x = 2 * cosx * cosx-1 = 1-2 * SiNx * sinxcos (x - π / 4) = - sin (x - π / 4 + π / 2) = - sin (x + π / 4) sin (x + π / 4) * sin (x + π / 4) = SiNx * sinxasinx + bcosx = under the root sign (a * a + b * b) sin (x + angle), where Tan angle

Function y = cosx- The value range of 3sinx is______ .

∵ function y = cosx-
3sinx=2[1
2cosx-
Three
2sinx]=2sin（π
6-x），-1≤sin（π
6-x）≤1，
∴-1≤2sin（π
6-x）≤2，
So the answer is: [- 2,2]

The value range of y = cosx radical 3sinx RT solution

Y = cosx radical 3sinx
=2 (1 / 2cos [- x] + radical 3 / 2Sin [- x])
=2sin（π/6-x)
be
-2

The value range of the function y = radical 3sinx + cosx, X ∈ [- 6 parts π, 6 parts π] is y=2(√3/2sinx+1/2cosx) =2(sinxcosπ/6+cosxsinπ/6) =2sin(x+π/6) -π/2

y=2(√3/2sinx+1/2cosx)
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
-π/6

Let a = (Radix 3sinx, cosx), B = (cosx, cosx), and let f (x) = vector a * vector B. write the minimum positive period of function f (x)

F (x) = radical 3sinx * cosx + cosx * cosx = radical 3 / 2sin2x + 1 / 2 (2cosx ^ 2-1) + 1 / 2 = radical 3 / 2sin2x + 1 / 2cos2x + 1 / 2 = sin (2x + 30 ") + 1 / 2, so the minimum period is 2 π / 2 = π

The maximum value of the function y = cosx + root 3sinx.)

Y = cosx + Radix 3sinx = 2 (1 / 2 * cosx + (Radix 3) / 2sinx) = 2 (sin30 ° cosx + cos30 ° SiNx) = 2Sin (30 ° + x)
So the maximum is 2

The function y = radical 3sinx cosx can be reduced to - with a maximum value of - and a minimum value of—— The function y = radical 3sinx + 4cosx can be reduced to - with a maximum value of - and a minimum value of——

The function y = radical 3sinx + 4cosx can be reduced to √ 19sin (x + Z)
Where Tanz = 4 / √ 3
There is a maximum value of √ 19 and a minimum value of - √ 19

The maximum, minimum and period of the function y = SiNx / 2 (Radix 3sinx / 2-cosx / 2)?

Y = SiNx / 2 (Radix 3sinx / 2-cosx / 2) = √ 3sinx / 2sinx / 2-1 / 2sinx
=√3/2-√3/2cosx-1/2sinx=√3/2+sin（x-2π/3）
The maximum value of the function is √ 3 / 2 + 1 and the minimum value is √ 3 / 2-1
Period T = 2 π

Monotone increasing interval of function y = cosx radical 3sinx /

Y = 2 [1 / 2cosx - (radical 3) / 2 * SiNx]
=2[cos60*cosx-sin60*sinx]
=2cos(60+x)
Let 60 + x = t, then the original formula = 2cost. We know that the monotone increasing interval is PI + 2K * PI

F (x) = 2cosx * sin (x + Pai / 6) + Radix 3sinx * cosx sin ^ 2x Find the monotone increasing interval of F (x);

For you to understand, I try not to jump f (x) = 2cosxsin (x + π / 6) + √ 3sinxcosx sin? X = 2cosx [sinxcos (π / 6) + cosxsin (π / 6)] + √ 3sinxcosx sin? X = 2cosx (√ 3sinx / 2 + 1 / 2cosx) + √ 3sinxcosx sin? X = √ 3sinxcosx + cos