If Tan a = 2, then the value of Sin & # 178; a / (1 + cos & # 178; a) is?

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• 1. Tan α = 2, find the value of [(sin α + cos α) / (sin α + cos α)] + cos & # 178; α
• 2. Use Maple to solve the equation x^5+x^4−12x^3−21x^2+x+5=0 y^5+y^4−16y^3+5y^2+21y−9=0 y^5+y^4−24y^3−17y^2+41y−13=0 y^5+y^4−28y^3+37y^2+25y+1=0 10x^6-75x^3-190x+21=0 All the previous quintic equations have radical solutions The last one, I don't know if there is. If there is, we need radical solution No, I hope it can be solved with a special function, like this z^5+z^4-e^6=0 z=exp(6/5)*hypergeom([-1/5,1/20,3/10,11/20],[1/5,2/5,3/5],256/3125*exp(-6)) +2/25*exp(-6/5)* hypergeom([1/5,9/20,7/10,19/20],[3/5,4/5,7/5],2/3125*exp(-6)) -4/125*exp(-12/5)* hypergeom([2/5,13/20,9/10,23/20],[4/5,6/5,8/5],256/3125*exp(-6)) +7/625*exp(-18/5)* hypergeom([3/5,17/20,11/10,27/20],[6/5,7/5,9/5],256/3125*exp(-6)) -1/5
• 3. On the proof of matrix complex field, we will add 1-2 times points Let a be a matrix of order n over a complex field 1) A is similar to a matrix in the form of: λ1 c12 c13 ... c1n 0 λ2 c23 ... c2n 0 0 λ3 ... c3n ... ... ... ... ... 0 0 0 ... λn 2) A has n eigenvalues (multiple roots count multiple numbers) in complex field, and if λ 1, λ 2,..., λ n are all eigenvalues and f (x) is any polynomial in complex field, then f (λ 1), f (λ 2),..., f (λ n) are all eigenvalues of F (a)
• 4. Let a be a matrix of order n over the complex field C It is proved that there exists an invertible matrix P of order n on C such that P ^ - 1AP = R1 A12. A1N 0 a22 .a2n . 0 an2 .ann
• 5. Higher algebra A is a matrix of order n over a complex field, R1, R2,..., RN are all eigenvalues of a (multiple roots are calculated by multiplicity) proof (1) if f (x) f (R1) The higher algebra A is a matrix of order n over a complex field. R1, R2,..., RN are all the eigenvalues of A. This paper proves that (1) if f (x) is a polynomial of degree greater than 0 on C, then f (R1), f (R2),... F (RN) are all the eigenvalues of F (a). (2) if a is invertible, 1 / R1, 1 / R2,..., 1 / RN are all the eigenvalues of a ^ - 1
• 6. Find I + root 2 in the rational number field Q irreducible polynomial, you master please tell me
• 7. It is proved that there exists an irreducible polynomial f (x) over the field of rational numbers, such that f (a) = 0
• 8. It is proved that irreducible polynomials with real roots in rational number field must be quadratic polynomials
• 9. X ^ 4 + 1 is decomposed into irreducible polynomials over the rational field
• 10. How to solve polynomial equation on complex field by numerical method I have a question to ask you, that is, how to write a program to solve the polynomial equation in the complex field (for example, f (x) = A2 * x ^ 2 + A1 * x + A0 = 0). Now I use the argument principle (in short, I integrate f '(x) / F (x) on the complex plane. If there is an internal solution, the integral is not zero, otherwise it is zero), The solution is determined by continuously narrowing the integral range. However, for the higher order (greater than 10 orders), it is not enough. Is there any algorithm improvement that can improve the accuracy and speed?
• 11. Sin α + cos α = 1 / √ 2 find the value of Tan & # 178; α + 1 / Tan & # 178; α
• 12. If Tan θ = 2, then the value of 1 / (Sin & # 178; θ - cos & # 178; θ) is
• 13. What is the running result of maple ('a: = ', 245674)
• 14. High score with maple to do a calculus problem! Consider the following function on the interval [0, π/2]. f (x) = √ 2x  cos8(2x) (a) approximate the area under F &; (x) on the given interval using midpoints with n = 10 (b) compute the definite integral of F ｛ 8201; (x) on the interval [0, ｛ 8201; π / 2] (c) find the absolute value of the error involved in estimating the area under F &; (x) on the given interval using a Riemann sum with midpoints and N = 10 (d) Using trial and error,determine the smallest number n of subintervals such that the absolute error of the midpoint Riemann sum with respect to the exact value of the area is less than 0.0005. 2X times (COS (2x)) ^ 8 under the root of the equation
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• 17. Maple / Matlab symbolic operation There is a problem for a long time Is there any way to define an n-dimensional vector (or matrix) in MATLAB or maple, but n does not need to be assigned, and then symbolic operation? For example, I need to derive a function: l = 0.5 * w (T) · V · W, Where W is a variable, an n-dimensional vector, w (T) is its transpose vector; V is an n * n coefficient matrix; n > 1 is an integer In the symbolic operation of maple or MATLAB, can l be derived without n assignment? The derivation of L is very simple. It's a general formula. The problem is how to do symbolic operation on a general formula like this in the program?
• 18. How to calculate the binary value of 110.110... With maple 110.110... Is a decimal with infinite cycles
• 19. cos(a+β)=3/5,cos(a-β)=12/13,0
• 20. First, cos (a + b) = 4 / 5. Cos (a-b) = - 4 / 5. A + B ∈ [7pi / 4,2pi]. A-B ∈ [3pi / 4, PI]. Cos2a =? Second, prove tan（ The second problem proves that Tan (θ + π / 4) = [Tan θ + 1] / [1 - Tan θ]