The minimum value of function y = sin ^ 2x + 2 / sin ^ 2x on (0. π / 2]

Y = x + 2 / X decreases at (0, √ 2)
And 0

What is the minimum value of the function f (x) = sin (2x - π / 4) in the interval [0, π / 2]?

∵x∈【0,π/2】
∴2x-π/4∈[-π/4,3π/4]
When 2x - π / 4 = - π / 4, the minimum value is sin (- π / 4) = - √ 2 / 2;
I'm very glad to answer your questions. Skyhunter 002 will answer your questions
If you don't understand this question, you can ask,

The square of X - x + 1 / 2 x = 7. To find the fourth power of x plus the second power of X + 1 / 2 x, we need to use the reciprocal method

X/(X^2-X+1)=7,
7X^2-7X+7=X,
7x ^ 2-8x + 7 = 0 (the equation has no real root)
X + 1 / x = 8 / 7 (divide both sides by 7x)
∴(X+1/X)^2=64/49
X ^ 2 + 1 / x ^ 2 = - 34 / 49 (reason for no real root)
X^2/(X^4+X^2+1)
=1 / [x ^ 2 + 1 / x ^ 2 + 1] (both numerator and denominator are divided by x ^ 2)
=1/(-34/49+1)
=49/15.

RELATED INFORMATIONS

1. Given x-3x + 1 = 0, find x + X-2 and X + x-4
2. Given that the x power of 10 is 20 and the Y power of 10 is 1 / 5, then the x power of 9 / 3 is 2Y=
3. Given that f (x) = e ^ x-ax-1, if f (x) increases monotonically in the domain R, the value range of a is obtained Let f (x) = e ^ x-ax-1, 1. If f (x) increases monotonically in the domain R, find the value range of A 2. If f (x) decreases monotonically on (negative infinity, 0) and increases monotonically on [0, positive infinity), find the value of A
4. The quadratic equation of one variable (3x + m) ^ 2 = n (x-3) ^ 2 is reduced to a general form The univariate quadratic equation (3x + m) ^ 2 = n (x-3) ^ 2 is reduced to a general form, which is a univariate quadratic equation about X, and Mn is a constant
5. When a ＜ 0, B ＜ 0 - A + 2 √ ab-b is reduced to what?
6. Write the simplest "and not" expression of logic function according to the following truth table A B C D F A B C D F 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1
7. Simplification of two lane Karnaugh Map Q: simplify the logical function to the simplest and or, where F = ∑ (M5. M6. M7. M8. M9), and the given constraint condition is M10 + M11 + M12 + M13 + M14 + M15 = 0 Simplify the logical function to the simplest or and F = ∏（M1.M2.M3.M6.M7.M9.M11.M13）
8. What's the difference between Boolean algebra operation and logic algebra operation? Can you list some formulas?
9. In RT triangle ABC, angle c = 90 °, a: C = 3:5, B = 12, find a and C?
10. As shown in the figure, in △ ABC, ∠ a = 40 ° and ∠ ABC = ∠ ACB, the middle vertical line (please draw with a compass and ruler) on the side of AB intersects AC at D and ab at e, connecting BD, (1) Explain why △ ade is congruent with △ BDE (2) Finding the degree of ∠ DBC
11. Why is the n-th power of 2 minus 1 divided by 7 equal to N divided by 3?
12. m3(m-2n)=n3(2m-n)=? Factorization problem
13. When x = ~ 2, a times the fifth power of x plus B times the third power of x plus CX minus 1 equals 5? Please help... Urgent!
14. The density of human body is about 10 cubic meters, and the mass of one person is 50kg My calculation process is v = m / P = 50kg / 1000kg / M m3, but the result is 1 / 20 m3. I don't think the data is correct
15. The average density of human body is about 1.06g/cubic centimeter, which should be 1.06g/cubic centimeter____ Kg / m3, a middle school student with a mass of 50kg, its volume is ____ Cubic meter____ Cubic decimeter_____ Cubic centimeter
16. The density of the human body and the density of water, According to Archimedes' principle, if the human body falls into the water and the water discharged is larger than the human body, then the human body will float on the water surface. If the density of the human body is higher, or the density of the water is higher, why do some people sink and others float In addition, in the fresh water of sea water, does the sinking of human body have something to do with floating
17. An elephant weighs 600 kg. The contact area between the foot and the ground is 600 square centimeters. How much pressure does the elephant exert on the ground when it stands on the ground with four feet?
18. The weight of an elephant is 5000 kg, and the area of each foot is 600 square cm
19. The density of a brick is 2.5 × 10 cubic kg / m3, and the maximum pressure it can bear is 7.35 × 10 quintic PA The maximum pressure that the ground can bear is 1.5 × 10 cubic Pascal?
20. The density of a brick is 2.0 g per cubic centimeter, and the maximum pressure it can bear is 9.0 × 10 cubic Pascal. How many meters can be built with this brick? Take the whole number