Formulas of trigonometric functions's reciprocal relation table trigonometric function: quotient relation: square relation: tan α cotα =1sin α CSC α =1sin α secα =1sin α/cos α = tan α = sec α/CSC α cos α/sin α = cot α = CSC. Secα sin2alpha+cos2alpha =11+tan2alpha = sec2alpha1+cot2alpha = csc2alpha (hexagonal mnemonic method: the graphic structure is "winding tangent, Zuo Zheng right remainder middle tangent,1"; The product of two functions on the diagonal is1; The sum of squares of trigonometric function values of two vertices on the shadow triangle is equal to the square of trigonometric function value of the next vertex; The trigonometric function value of any vertex is equal to the product of the trigonometric function values of two adjacent vertices. " ) inductive formula (formula: odd variable pairs, symbols look at quadrants. )sin(-α)=-sinαcos(-α)= cosαtan(-α)=-tanαcot(-α)=-cotαsin(π/2-α)= cosαcos(π/2-α)= sinαcot(π/2-α)= tanαsin(π/2+α)= cosαcos(π/2+α)=-sinαtan(π/2+α) Formula of trigonometric function =-cotαcot(π/2+α)=-tanαsin∈Z) General formula of sum and difference of two angles sin (α+β) = sin α cos β+cos α sin β sin (α-β) = sin α cos β-cos α sin β cos (α+β) = cos α cos β. +β)=———— 1-tanαtanβtanα-tanβtan(α-β)=———— 1+tanαtanβ2 tan(α/2)sinα=———— 1+tan 2(α/2) 1-tan 2(α/2)Cosα=———— 1 +tan 2(α/2)2 tan(α/2)tanα cosine sum tangent formula sin2alpha = 2sinα cos α cos2alpha = cos2alpha-sin2alpha = 2cos2alpha-1=1-2sin2α tan2alpha = ————/kloc-0. Tanα-Tan3α Tan3α = ——1-3Tan2α trigonometric function sum and difference product formula; The sum and difference formula of trigonometric function α+β α-β sin α+sin β = 2sin ————————— 22α+β α-β sin α-sin β = 2cos-β cos α+cos β = 2cos ———————————— 22α+β α-β cos α-cos β =-2sin. +sin (α-β)] 21cos ABA = ABA = {x | x ∈ a, and X ∈ B} AB = {or X ∈ B} card (ab) = card (A)+ card (B)- card (. Then p (2) the relationship among the four propositions (3) A is a necessary condition for B. A is a necessary and sufficient condition for B. The property index and logarithm (1) of the function of B define the domain, range and corresponding rules (2) monotonicity for any x 1, x2∈D if x/kloc-0. Let f(x) be a increasing function on d If x 1 < x2f(x 1) > f(x2), let f(x) be a subtraction function on d (3) If parity is any x in the definition domain of function f(x), if f (-x) = f (x. Let f(x) be odd function (4). If there is a constant t, f(x+t) = F (x), then f(x) is called a periodic function (1). The meaning of positive fractional exponential power is negative fractional exponential power. The meaning of negative fractional exponential power is (2) loga (Mn) = logam+loganlogam = nlogam (n ∈ r) exponential function logarithmic function (1) Y = ax. A≠ 1) is called exponential function (2)x∈R, Y > 0. When the image passes through (0, 1) A > 1, X > 0, y >1; X < 0，0 < y < 10 < a < 1，X > 0，0 < y < 1； When x < 0, y > 1A > 1, y = ax is increasing function 0 < A < 1, y = ax is a decreasing function (1) y = logax (A > 0, a ≠/kloc. 0 < x < 1 and y < 00 < a < 1, x > 1 and y < 0; 0 < x < 1, y > 0a > 1, y = logax is increasing function 0 < a < 1, y = logax is exponential equation of decreasing function and logaf (x) = BF (x) = AB (a > 0, A≠ 1) logaf (x) = logag (x) f (x) = g (x) > 0 (a > 0, A≠ 1) Substitution formula f (ax) = 0 or f (logax) = 0 Basic concept of a series arithmetic progression (1) General formula of a series an = f (n) (2) Recursive formula of a series (3) Relationship between the general formula of a series and the sum of the first n terms an+/. B arithmetic 2A = A+B M+N = K+L AM+An = AK+Al geometric series common summation formula An = A 1QN _ 1A, g, b equal proportion G2 = AB M+N = K+L Aman = Akal inequality basic properties important inequality A > BB < AA b>c a>c a>b a+c>b+c a+b>c a>c-b a>b，c>d a+c>b+d a>b，c>0 ac>bc a>b，c0，c>d>0 acb>0 dn>bn(n∈Z，n> 1) a>b>0 >(n∈Z， N > 1)(A-B)2≥ 1 To prove A < B, it is only necessary to prove that the synthesis method is a method to derive the inequality to be proved (from cause to effect) from the known or proven inequality according to the nature of inequality. The analytical method starts from seeking the sufficient conditions for the conclusion to be established, and gradually seeks the sufficient conditions for the required conditions to be established until the required conditions are known to be correct, which obviously shows the complex algebraic form of "holding the cause" A+Bi = C+DIA = C, B = d (a+bi)+(c+di) = (a+c)+(b+d) I (a+bi)-(c+di) = (a-c)+(b-d) I (a+bi) (c+di) = (AC no. And b 1≠b2 l 1 coincides with l2 or k 1 = K2 and b 1 = B2L 1 intersects with l2 or k 1=k2 =-65438. 2. The standard equation of conic elliptic circle (X-A) 2+(Y-B0) (B2 = A2-C2 The center is (a, b) and the radius is R. The general equation X2+Y2+DX+EY+F = 0, where the center is () and the radius r (1) is judged by the distance d from the center to the straight line and the radius r of the circle. | mf2 | = a-ex0 hyperbola parabola hyperbola focus f 1 (-c, 0), F2(c, 0) (a, b > 0, B2 = C2-a2) eccentricity alignment equation focus radius | mf 1 | = ex0+a, | mf2 |. 0) Translation of the coordinate axis of the focus F directrix equation, where (h, k) is the coordinate of the origin of the new coordinate system in the original coordinate system.

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