![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Let f (x) = (sin ^ 4 x-cos ^ 4 X-5) / (cos2x + 2); (a) prove that f (x) = 3 / (2 sin ^ 2 x-3) - 1 (b) find the range of F (x)
f(x)=(sin^4 x-cos^4 x-5)/(cos2x+2)
=(sin^2 x-cos^2 x-5)/(cos2x+2)
=-（cos2x+5）/（cos2x+2）
=-1-3/（cos2x+2）
=-1-3/（1-2sin^2 x+2)
=3/(2sin^2x-3)-1
It's over
b）、f（x）==3/(2sin^2x-3)-1,sin^2x∈【0,1】
So 2Sin ^ 2x-3 ∈ [- 3, - 1]
So f (x) max = - 2, f (x) min = - 4
That is, the range of F (x) is [- 4, - 2]
RELATED INFORMATIONS
- 1. Let f (x) be continuous on [0, π], and be derivable in (0, π). It is proved that there exists ξ ∈ (0, π) such that f '(ξ) sin ξ + 2F (ξ) cos ξ = 0
- 2. Let f (x) be continuous on [0, π], and be derivable within (0, π). It is proved that there exists ξ ∈ (0, π) such that f '(ξ) sin ξ + F (ξ) cos ξ = 0
- 3. It is known that P is a point outside the parallelogram ABCD, the diagonal AC and BD intersect at O, and AP ⊥ CP
- 4. A mathematics application problem is urgent! Xiao Liang's house painted the room and finished it after 10 days; he used 150 liters of certain paint, and the paint cost was 4800 yuan; the painting area was 130 square meters, and the final settlement of the payment was as follows: 1. According to the work, each worker was 30 yuan (one worker worked a day); 2. According to the paint cost, 30% of the paint cost was used as the payment; 3. According to the painting area, Pay 12 yuan per square meter. Which plan do you think is the most economical--
- 5. The area of a circle is 78.5cm. Find the circumference,
- 6. There is a wall clock in the school hall. The length of the hour hand from the fixed point to the tip of the needle is 25cm, which is the same as how many centimeters the needle end of the hour hand walks day and night?
- 7. Cut off a rectangle 2cm wide from the square sheet, and the remaining area is 48cm2. Then the area of the original square sheet is () A. 9cm2B. 68cm2C. 8cm2D. 64cm2
- 8. Physics problems in grade two The total mass of an empty bottle filled with water is 700g. If 108G metal block is put into the empty bottle, the total mass is 768g 1. Volume of metal block 2. The density of this metal block You can't do it with buoyancy. I haven't learned it
- 9. The distance between the two feet of a compass is 5cm. If you draw a circle, what is the circumference of the circle______ What is the area of this circle______ ．
- 10. The maximum and minimum of sine function y = - 6sin (2X-4 π) + 1 Seeking process
- 11. It is proved that ∫ (0, π / 2) (f SiN x / (f SiN x + F cos x) DX = π / 4
- 12. Let f (x) = cos X. prove that (COS x) '= - sin
- 13. Cos (x + 6 π) = 4 / 5 why sin (x + 6 π) = 3 / 5
- 14. If f (3sinx) = cos square X / sin square x is known, find f (x)= I'm a beginner. Please elaborate
- 15. Y = cos square x-sin square x + 3sinx Find the maximum and minimum
- 16. Simplification: 1, sin (x - π / 3) - cos (x + π / 6) + √ 3cosx =? 2, known, sin α + sin β = √ 2 / 2, find the value range of cos α + cos β
- 17. If a belongs to {0, π / 2} and COS square a + sin {π / 2 + 2A} = 1 / 2, then Tana =?
- 18. Cos2 β = - (1 / 2), then sin β=
- 19. The result of 2 + cos2-sin1 ^ 2 under the root sign is A cos1 B sin1 C √3 *cos1 D -√3*cos1
- 20. It is known that a is the third quadrant angle, and COS (A / 2) + sin (A / 2) = - (√ 6) / 3, √ (1 + COSA) = - {2Sin (A / 2) 1 ask me to calculate the value of COS (A / 2) - sin (A / 2) 2 question: （cos(a/2)*cos(a+3.14/4))/(1+tan(a/2))