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sin（x-y）cosy+cos（x-y）siny=?
sin（x-y）cosy+cos（x-y）siny
=sin(x-y+y)
=sinx
Let α, β, y ∈ R, then sin α + sin y = sin β, cos α + cosy = cos β, then α - β
Sin α + siny = sin β sin α - sin β = - siny, the squares of both sides get Sin & # 178; α + Sin & # 178; β - 2Sin α cos β = Sin & # 178; y ① cos α + cosy = cos β cos α - cos β = - cos & # 178; α + cos & # 178; β - 2cos α cos β = cos & # 178; y ② ① + ② get 1 + 1-2
Given that the point (m, n) is on the image of inverse scale function y = - 2 / x, then the value of Mn is
The point (m, n) is on the image of inverse scale function y = - 2 / X
When x = m, y = n
So n = - 2 / m
So Mn = - 2
The image of the first-order function y = ax + B intersects with the x-axis and y-axis at points m and N respectively, and intersects with the image of the inverse scale function y = KX at points a and B. passing through point a, AC ⊥ x-axis and AE ⊥ Y-axis respectively, the perpendicular feet are C and e respectively; passing through point B, BF ⊥ x-axis and BD ⊥ Y-axis respectively, the perpendicular feet are f, D, AC and BD, intersecting with point K respectively, connecting CD (1) If points a and B are on the same branch of the image with inverse scale function y = KX, as shown in Fig. 1, we try to prove that: (1) s quadrilateral AEDK = s quadrilateral cfbk; (2) if points a and B are on different branches of the image with inverse scale function y = KX, as shown in Fig. 2, then are an and BM equal? Try to prove your conclusion
(1) It is proved that: ① ∵ AC ⊥ x-axis, AE ⊥ y-axis, ∵ quadrilateral aeoc is rectangular. ∵ BF ⊥ x-axis, BD ⊥ y-axis, ∵ quadrilateral bdof is rectangular. ∵ AC ⊥ x-axis, BD ⊥ y-axis, ∵ quadrilateral AEDK, dock, cfbk are rectangular. (1 point) ∵ OC = x1, AC = Y1, x1 · Y1 = k, ∵ s rectangular aeoc = OC · AC = x1 · Y1 = k ∵ of = X2, FB = y2 = k, ∵ s rectangular bdof = of · FB = x2 · y2 = K Rectangular aeoc = s rectangular bdof. ∵ s rectangular AEDK = s rectangular aeoc-s rectangular dock, s rectangular cfbk = s rectangular bdof-s rectangular dock, ∵ s rectangular AEDK = s rectangular cfbk. (2 points) ② it is known from (1): s rectangular AEDK = s rectangular cfbk. ∵ AK · DK = BK · CK. ∵ akck = bkdk. (4 points) ∵ AKB = ∵ CKD = 90 degree, ∵ AKB ∵ CKD. (5 points) ∵ CDK = ∵ Abk. ∥ ab ∥ CD. (6 points) ∥ AC ∥ Y axis, The parallelogram acdn is a parallelogram. An = CD. (7 points) similarly BM = CD. (8 points) (2) an and BM are still equal. (9 points) ∵ s rectangle AEDK = s rectangle aeoc + s rectangle ODKC, s rectangle bkcf = s rectangle bdof + s rectangle ODKC, and ∵ s rectangle aeoc = s rectangle bdof = k, ∵ s rectangle AEDK = s rectangle bkcf. (10 points) ∵ AK · DK = BK · CK. ∵ ckak = dkbk. ? k = ∠ K, ∩ CDK ∽△ ABC. ∽ CDK = ∽ ABC. ∽ ab ∥ CD. (11 points) ∵ AC ∥ y-axis, ∽ quadrilateral andc is parallelogram. ∽ an = CD. Similarly, BM = CD. ∽ an = BM. (12 points)
It is known that when x = 5, the quadratic function f (x) = ax ^ 2 + BX + C obtains the minimum, the first n terms of the arithmetic sequence an and Sn = f (n),
a2=-7,
1. Find the value of a, B, C
2. General term formula of sequence an
From the meaning of the title, - B / 2A = 5, that is, B = - 10A; ①
If an is an arithmetic sequence, then Sn = (a1 + an) n / 2 = f (n) = an ^ 2 + BN + C,
So C = 0, a1 + an = 2axn + 2B, ②
When n = 2, a1 + A2 = 4A + 2B = a + B-7,
That is 3A + B = - 7, ③
① A = 1, B = - 10,
Dai Ren (2) got an = 2n-11
As shown in the figure, the image of inverse scale function y = KX (k > 0) intersects the edges AB and BC of rectangular oabc at points D and e respectively. (1) if k = 2, calculate the area of △ ODA. (2) if B (3, a), D (1, a), use the algebraic expression containing a to express the ordinate of point E. (3) if point E is the midpoint of BC, prove that point D is the midpoint of ab
(2013 &; Neijiang) as shown in the figure, the image with inverse scale function y = K / X (x ＞ 0) passes through the intersection m of diagonal lines of rectangular oabc, and is respectively located at AB, AB, and
As shown in the figure, the inverse scale function y = K / X
The image of (x > 0) passes through the intersection m of the diagonal of the rectangular oabc and intersects at points D and e at AB and BC respectively. If the area of the quadrilateral odbe is 9, then the value of K is 0
Young students, this question examines the geometric meaning of the coefficient K of the inverse proportion function. If you cross any point on the hyperbola and make a vertical line to two coordinate axes respectively, the area of the rectangle surrounded by the coordinate axis is equal to | K |. This knowledge point is the key point of the senior high school entrance examination. You should master it
As shown in the figure, point C is on ⊙ o with ab as the diameter, CD ⊥ AB is on point P, let AP = a, Pb = B. (1) find the length of chord CD; (2) if a + B = 10, find the maximum value of AB, and find the value of a and B at this time
(1) ⊙ AB is the diameter of ⊙ o, CD ⊥ AB is at point P, in right triangle ACB, according to the projective theorem, PC2 = AP · Pb, ∵ AP = a, Pb = B, ∵ CD = 2pc = 2pc2 = 2Ab, (2) ∵ a + B = 10, ∵ ab ≤ (a + B2) 2 = 25, if and only if "a = b = 5" = "holds
If the function y = KX + B passes through the point (1, - 2), then its intersection coordinates with the Y axis are (0, - 4) and parallel to the straight line y = - 2x, then the function expression is y =? When x = 1, y =?
y=-2x-4
Given that the line y = KX + B is parallel to y = - 1 / 2x, and the ordinate of the intersection point with y axis is 3, then the function expression is
Parallel to y = - 1 / 2x, then k = - 1 / 2
If the ordinate of the intersection point with the Y axis is 3, then the intercept B = 3
So y = - 1 / 2x + 3
RELATED INFORMATIONS
- 1. A brief and detailed process of transforming trigonometric function sin (X-Y) cosy + cos (X-Y) siny
- 2. If the maximum value of quadratic function f (x) = x2 + 4x + 6 on [M, 0] is 6 and the minimum value is 2, then the value range of real number m is______ ．
- 3. Is f (x) = cos (x + π) even function
- 4. If the function f (x) = 2cos (2x + ϕ) is odd and is an increasing function on (0, π 4), then the real number ϕ may be () A. −π2B. 0C. π2D. π
- 5. The range of the function y = 5-6cosx-sin & sup2; X is Writing process
- 6. Finding the range of function y = Sin & # 178; x-2sinx-1
- 7. The range of y = Sin & # 178; X + 2sinxcosx + 1
- 8. The range of y = sin square x + 4cos square x-4
- 9. It is known that the image of quadratic function y = ax05 + BX + C passes through points a (3,0), B (2, - 3), C (0. - 3) (1) The analytic formula and the axis of symmetry have been worked out as y = x & # 178; - 2x-3 and x = 1 respectively (2) Point P starts from point B and moves along the line BC to point C at the speed of 0.1 unit per second. Point Q starts from point O and moves at the same speed The velocity moves along the line OA to point A. when one of the moving points reaches the end point, the other stops moving. Let the moving time be T seconds 1. What is the value of T when the quadrilateral abpq is an isosceles trapezoid, 2. Let the intersection of PQ and the axis of symmetry be m, let the parallel line passing through M be the intersection of X axis and ab at n, and let the area of the quadrilateral anpq be s , find the analytic expression of the function of area s with respect to time t, and point out the value range of T,
- 10. Only function FX = AX2 + 1 / BX + C (a, B, C ∈ z) is odd, and F1 = 2, F2 < 3, find a, B, C
- 11. We know that vector a = (cosx, SiNx), vector b = (cosy, siny), | A-B | = 2 * & 5 / 5, 1. Find the value of COS (X-Y) 2. If 0 Please write the specific steps (O & # 180; &;'O) ぉ (O & # 180; Д'o) は (O & # 180; ω'o) ょ
- 12. It is known that f (x) is an even function defined on R, and the image of y = f (x) is symmetric with respect to the line x = 2. It is proved that f (x) is a periodic function
- 13. It is proved that the periods of F (x + a) = - f (x) and f (x + a) = 1 / F (x) are 2A The approximate step is f (x + 2a) = f [(x + a) + a] = - f (x + a) = f (x), so f (x + 2a) = f (x), so the period is 2A F (x + 2a) = f [(x + a) + a] = 1 / F (x + a) = f (x), so f (x + 2a) = f (x), so the period is 2A These are the teacher's steps, but I can't understand them now,
- 14. Given the function f (x) = 2Sin (x + π / 3) - 2sinx, X belongs to - π / 2,0 (1) If cosx = √ 3 / 3, find the value of function f (x) (2) Finding the range of function f (x) I'm in a hurry
- 15. Draw the image of function y = 1 / 2x + 1 in the given rectangular coordinate system (fill in the following table first, and then draw the line of points) x=-3 y=?…… x=3 y=?
- 16. It is known that the odd function f (x) = - X's square + 2x (x > 0) 0 (x = 0) x's Square = MX (x)
- 17. The range of the image of the function y = LG (2 + x) + LG (2-x) with respect to the symmetric function f (x) = LG (x2-2x + 1)
- 18. It is known that the function f (x) defined on [0,1] satisfies the following three conditions simultaneously It is known that the function f (x) defined on [0,1] satisfies the following condition: when x1 ≥ 0, X2 ≥ 0, X1 + x2 ≤ 1, f (x1 + x2) ≥ f (x1) + F (x2) always holds, and whether the function g (x) = 2 ^ X - 1 satisfies this condition in the interval [0.1]
- 19. The function f (x) is an even function on R, and is a decreasing function on (- 00,0). Compare the size of F (- 7 / 8) and f (2a ^ 2-A + 1)
- 20. When x belongs to R, the function y = f (x) satisfies f (2002 + x) + F (2004 + x) = f (2003 + x), and f (1) = Lg3 / 2, f (2) = LG15, then f (2007) =?