Given SiNx + siny = 1 / 3, find the maximum and minimum of SiNx cosy * cosy

SiNx = 1 / 3-siny, so SiNx - (cosy) ^ 2 = (1 / 3-siny) - [1 - (siny) ^ 2] = (siny) ^ 2-siny-2 / 3 = (siny-1 / 2) ^ 2-1 / 4-2 / 3siny ∈ [- 1,1]. When siny = - 1, (siny-1 / 2) ^ 2 obtains the maximum value of 9 / 4, and SiNx - (cosy) ^ 2 obtains the maximum value of 4 / 3

RELATED INFORMATIONS

1. Given the function f (x) = sin square meter x + 2sinxconx cos square x, find the monotone increasing interval of function f (x)
2. Given that the function f (x) satisfies f (x + y) + F (X-Y) = 2F (x) · f (y) & nbsp; (x ∈ R, y ∈ R), and f (0) ≠ 0, we try to prove that f (x) is an even function
3. Let f (x) = Sin & # 178; (x + π / 4) if a = f (lg5), B = f (LG1 / 5), then a+b=0 a+b=1 a-b=0 a-b=1
4. If f (x) = sin (2x + Pai / 3), then () A. The image of F (x) is symmetric with respect to the line x = Pai / 3 B. The image of F (x) is symmetric with respect to (PAI / 4,0) C. The image of F (x) is shifted to the left by Pai / 12 units to obtain the image of an even function D. The minimum positive period of F (x) is Pai and is an increasing function on [0, Pai / 6]
5. Given (1-tana) / (2 + Tana) = - 1 / 4 (1), find the value of Tan (a + π / 4) (2) find the value of (1 + sin2a) / (2cos ^ 2A + sin2a)
6. Given that Tan (π / 4-A) = 1 / 3, a belongs to (0, π / 4). (1) find the value of (a) = (sin2a-2cos ^ 2a) / (1 + Tana) (2) If B belongs to (0, π / 2), and sin (3 π / 4 + b) = - radical 5 / 5, find the value of a + B
7. It is known that Tan (a + 45) = - 1 / 2, (90
8. Given Tan (a + π / 4) = - 1 / 2, π / 2 & lt; a & lt; π, find the value of (sin2a-2cos ^ 2a) / √ 2Sin (a - π / 4)
9. Given Tan a = - 1 / 3, find sin2a cos ^ 2A
10. It is known that Tan (a pie / 4) = 1 / 2 and - Pie / 2
11. How to find the maximum and minimum value of y = cos2x + SiNx, y = 1-2 (the square of SiNx) + SiNx = 2 (the square of sinx-1 / 4) + 9 / 8
12. If f (Sin & nbsp; x) = 3-cos & nbsp; 2x, then f (COS & nbsp; x) = () A. 3-cos 2xB. 3-sin 2xC. 3+cos 2xD. 3+sin 2x
13. In order to get the image of function y = cos (2x + π 3), we only need to change the image of function y = cos 2x to___ Parallel movement___ A unit
14. Finding the maximum and minimum of Y by the function y = Cos2 (square) x-4sinx
15. The maximum value of the function f (x) = cos ^ 2x + 4sinx + 3 is
16. Given the function FX = ︱ SiNx ︱ cosx - sin2x-1 (1), find the maximum value of function FX (2) If the function FX has exactly 2014 zeros on (0. MX), find the value range of M
17. Given the function f (x) = SiNx (SiNx + √ 3cosx), find the minimum positive period of F (x)
18. Find the minimum positive period and minimum value of the function y = sin4x + 23sinxcosx-cos4x, and write the monotone increasing interval of the function on [0, π]
19. It is known that the minimum positive period of the function f (x) = cos ^ 2wx + sinwx * coswx-1 / 2 (W > 0) is π
20. Given SiNx + siny = cosx + cosy = 1 / 2007, what is SiNx + cosx = then