Find all solutions of cos2x + cosx = 0. + na, 3 + na, nK, wherenis an integer + 2nn, where n is an integer 3 2n + 2na, 3 5n + 2nn, 3 + 2na, n+ 2nn, where n is an integer 3 + 2na, 3 5л + 2na, n + 2nn, where n is an integer 3 - + 2nn, 3 3n + 2na, n+ 2nA, where n is an integer

Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

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Q: Find the z tronsfom of f(n) = a" cos (bn).

A: We have to find the z transform of the following.

Q: cos(-5x)+cos(9x) is equivalent to: cos(2x) Select one: not in the list O 2cos(7x) O 2sin(2x)…

A: Cos(-x)= cos(x)

Q: Find the 6th root of 12(cos120 + jsin120). O a. 0.52-jl.42 O b. 1.42+j0.52 O c. 1.42-j0.52 O d.…

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Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

Q: 6/155) cos 0, 1+ cos 29

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Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

Q: If z = 2 ( cos 2¥/3 + isin 2¥/3 ), then z^3=   i. 2 - i8√3 ii. -4 + i4√3 iii.-8-i√2 iv. -8 - i4

A: Using de-moivre's formula :

Q: For a Cauchy-Euler DE the roots of auxiliary are m = -3 ± 3i then Ye = x (c, cos(3 In x)+ c2 sin(3…

A: Using substitution of Cauchy Euler D.E.

Q: 2. an = 3 +- + cos(2nz) п 3. an = In(14n – n) – In(3n° + 2n² + 1) - |

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Q: Let A = ° -2 [23] eAt = e2t T eAt = e³t eAt = e³t e³¹ = cos(3t) [- sin(3t) cos(2t) sin(2t) [ e37 .…

A: A square matrix A is given. The objective is to find the value of eAt. If A=a-bba, then eAt=eatcos…

Q: If Z-1/v2+i/v2 then the value of conjugate of Z^5=?* O cos(3n/4) O 2sin(5n/4) O 2cos(5n/4) cos(5n/4)

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Q: 3 Find ALL solutions of cos 2x = 2 %3D

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Q: The set of solutions of y = -2e-* – 12 cos(4x) + 2 is given by: a) O 2e-* + 3 sin(4x) + 2x + C b) O…

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Q: 3 of u(a,9) = Cof"( 4y Cof' (+y then provethat ace +4u + Sin2ce=0

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Q: 4. Let z1 = 24(cos(75°) + i•sin(75°)) and z2 = 2(cos(15°) + i • sin(15°) ). Compute the %3D %3D…

A: SOLUTION-

Q: Determine whether Y1 = e', y2 = sin2t, ya = cos2t make up a fundamental set of solutions by finding…

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Q: Find all the roots of z²= - /3-j A z=2 (cos +j sin-) B z=/2 (cos (- =+ 2kn) +j sin ( 12 + 2kn)), 12…

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Q: 6. Find the general solutions of X' = AX with A = 5 4 Use X = eat [c1{Reß cos bt – Im ß sin bt}+…

A: According to the given information, it is required to find the general solution of X’ = AX.

Q: The particular solution to the DE y" - 3y' - 4y = -8et cos2t is a. lm { 4et+i2t / 5 + i } b. lm {…

A:

Q: Suppose that cos 8 = 5/13 and 3T/2 < 0 < 2n. (a) Compute sin 0. (b) Compute cos 20 Hint: cos 20 =…

A: ANSWER :

Q: If y=C,cos2x + C ,sin2x + 2sinx is the general solution of a certain nonhomogegeous LDE, which of…

A:

Q: Show that (cos x + isin x)n= cos nx + isin nx whenever n is a positive integer. (Here i is the…

A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

Q: What is the value of csc ( 1) 137 7T + cos( V3+2/2 O -V3-2/2 -V3+2/2 2 V3-2/2

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Q: π/2 0 /1-cos2xdx

A: solution:-∫0π21-cos2xdxwe know that cos2x-sin2x=cos2x1-sin2x-sin2x=cos2x1-cos2x=2sin2x

Q: ind all the exact solutions of  4sin 2x – 4sin x = 0 for x E[0 , 2pi).

A: Given  4sin2x-4sinx=0   x∈0;2π

Q: Give all exact solutions over the interval [0 , 360 ]. 2cos2 20 = 1 -– cos20 Select one: O a. 22.5°…

A: Let's find.

Q: Express as a product.cos 5t + cos 6t

A: Given : cos 5t + cos 6t

Q: Which of the following is NOT a solution of 2(1 - cos2x) - sin x = 1 over the interval [0, 2rt)? О…

A: Solving the problem by obtaining the all solutions of the system.

Q: cos 4x = cos 6y, which of the following is correct? 2x + 3y = 90⁰ 2x + 3y = 270⁰ 2x + 3y = 180⁰ 2x…

A: Given query is to find which statment is correct.

Q: 5. Find ALL degree solution of 3sin 0 + 3 = 2 cos' 0.

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Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Which of the following is a cubed root of (-/3 - 9? (A) 21°[cos(8z9) + i sin(8z9)] (B) 21[cos(7x/9)…

A:

Q: Let m be the number of solutions of sin (2x) + cos (2x) + cos x + 1 = 0 in 0<x< x< 1/1/2 and 7 7π n…

A: The roots of the equation: f(x)=0 are the values of x, where the graph of the function: y=f(x)…

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: Find all solutions in{ 0, 2m): cos² z – cos z=0

A:

Q: The square root of (1 2i) is (1) V5 (cos (+ 2n)+ i sin (5 + 2n")) for n = 0,1 COS (2) V5 (cos (+ 2)…

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: Express as a product a. cos 5t + cos 6t b. cos x + 2x

A: We have to express as a product  (a)  Cos 5t + Cos 6t We know that  CosC + CosD =…

Q: 3-Vx² +5 is co

A: f(x)=4-x3-x2+5,x≠2       =k, x=2

Q: Give the smallest two solutions of cos(2θ) = 0.4486 on [ 0,2π ).

A:

Q: Solve the equation on the interval 0 ≤ 0 < 2. 2 cos ²0 - 3 cos 0+1=0 O A. O B. O C. O D. ππ 5π 3'2'…

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Q: 2/2 00 (-1)" (2n + 1)³' COs nx 1°) Show that dr = Justify your reasoning. n=1

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Q: If z1 = 2 cis 30° and z2 = 4 cis (-60°) Find in modulus –argument form z,? x z2 (i) (ii) 3 Z1 Z2

A: Step:- 1 Let z be a complex number and modulus -argument form of z is z=r (cosθ + i sinθ); Here, r…

Q: Write cos 3x as a third-degree polynomial in cos æ. [Hint: Write cos 3x as cos (2x + x)] Select one:…

A: Given: cos(3x) = cos ( 2x + x )

Q: For a Cauchy-Euler DE the roots of auxiliary are m = -3 + 3i then Ye = x= (c, cos(3 In x)+ c2 sin(3…

A:

Q: Use Superposition approach to find the genral solution of the following equation: у" — 2у' + 3у - -6…

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Q: (a) Find all the solutions of cosh z = 4 (Hint: cosh z =

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Q: Which of the following are the solutions of tan²x+ secx = 1 on the interval [0, 2n)? %3D 2я 4я 3' 3…

A: for a quadratic equation ax2+bx+c=0 x=-b±b2-4ac2a