1 1. Prove the identity cosh2 r = 1 cosh 2x 2

Q: need help with attached, thanks

A: Given function and interval are,

Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 do. 1+8 cos? 0

A: Note:-  cosθ=eiθ-e-iθ2 Residue Theorem:- ∫Dfz dz =2πi ∑k Res fzk=2πi×sum of residues   Given that…

Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: A-Show that S 1, L{cos at} s2+a²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: 2a + acoth 2z ) dz \sin 3z a/2

A: We are given the integral: ∫a22a1sin 3z+a coth 2zdz Let I=∫a22a1sin 3z+a coth 2zdz I =∫a22a1sin 3z+a…

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: cos(3rk) In k 5k k 1

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Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

A:

Q: /2 1. (a) Use the Wallis cosine formula to evaluate cos' x dx. (b) Evaluate | 1 - dx by using…

A: Wallis's formula state that 1. if  n is odd and n≥3,then ∫0π2cosnxdx=23.45.67 . . . n-1n Therefore,…

Q: Question 4 Evaluate * 16" sin () (2n)! 3 n=0 given that cosh z 2n (2n)! n=0

A: Evaluate : ∑n=0∞16n sinnπ32n! It is given that, cosh z=∑n=0∞z2n2n!

Q: 3.(1) Show that (x) - J{«) )x cos 2.x

A: Consider the Bessel function, Jnx=xn2n Γn+11-x222n+2+x42·42n+22n+4-…             ...1 Substitute…

Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: 5. cos(M) = %3D 6. sin(L) = %3D 7. cos(L) = 30 34 %3D 8. tan(M) = %3D 16

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Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

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: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

A: Given

Q: *(+²–1) cos[cosh (In r")]dr 4.

A:

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

A:

Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: COs 05

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Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

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Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: Evaluate the iterated integral. π/4 cos(8) 1¹ Jo 3/² 3r² sin(8) dr de

A: Given: ∫0π4∫0cosθ3r2sinθdrdθ

Q: See image below....

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Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

A:

Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

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Q: 22: Evaluate Sea s cos²(y s) ds.

A: Solution:-

Q: Evaluate the integral. sin (3u + 7) du dv dw 0 00 2 O A. z cos 7 1 O B. 국COS 7 OC. 1? cos 7 1 O D. 1…

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Q: 1/2 cos t Evaluate the integral o dt. 4.- sin? t In a Give your answer in the form where a and b are…

A: Given: ∫0π2cost4-sin2tdt Let sint=xcost=dx Then sin0=0sinπ2=1 So, ∫0π2cost4-sin2tdt=∫01dx4-x2

Q: 8. Find all values of 0, if 0 is in the interval [0°, 360°) and cos 0 V3 2

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Q: 2n 1 (cos=0 0 +i sin e) + 10 2cosno eine

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: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: 4. Use the first Fundamental Theorem of Calculus to find 3r 2-1 dt 12 +1 sin 2z

A: Fundamental theorem of calculus Let us consider the continuous function f(x)  on the interval [a,b]…

Q: 5) Determine the following indefinite integral cos (3x) (1 – sin(3x))(2 – sin(3x)) -dx

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

A:

Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

A:

Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt