b. Determine real (e/z) in terms of x and y. C. Use Euler's formula to prove that expression; = cos z + i(sin z) d. Show that sin z is exists or not?

Q: A- Find all values of z such that sinh(z) = e'ő. B- Are |z], Img(z) analytic? Give reason.

A: Solution of the problem as follows

Q: Use the following conditions to find the exact value of tan(α - β).

A: Trigonometry: sinα=45,π2<α<πcosβ=513,0<β<π/2We need to find…

Q: b)Estimate the value of cos 0, at 0 = 5°with the help of the following table 0: 0° 10° 200 30° 40°…

A: If θ be an angle in a right-angled triangle, then the sine of the angle or sinθ is defined as the…

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Q: b)Estimate the value of cos 0, at 0 = 5°with the help of the following table 0⁰ 10⁰ 20⁰ 30⁰ 40⁰ 50⁰…

A: The given table is: θ 0 10 20 30 40 50 sinθ 0 0.1736 0.342 0.5 0.6428 0.766 We have to…

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Q: 1. (a) Use the Wallis cosine formula to evaluate [ cos' x dx.

A: We need to find  ∫0π2cos9xdx by using Wallis cosine formula. We know that,  Wallis formula ,  If  n…

Q: Find the quotient where z1 and z2 are given Z2 below. zi = 24 (cos(171°) + i sin(171°)) Z2 = 4…

A: z1=24(cos171°+isin171°)=24ei171°z2=4(cos51°+isin51°)=4ei51°

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A: ∫0π2sin x1+cos xdx Formula ∫xndx=xn+1n+1+C

Q: OBTAIN THE GENERAL SOLUTION 1. X cos? ydx = + tan ydy

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Q: Let z E C. Prove the following using concepts in C. (a) sin(-2) = – sin z (b) cos(-2) = cos z (c)…

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Q: Evaluate / cos(a0)d0 where a is a real number, and C is an arbitrary constant. sin(æ0) + C O a…

A: Solution-

Q: Given that sin t =1/2and 0 ≤ t <π/2, find the value of cos t using a trigonometric identity.

A: sin t =12and0≤t≤π2i.e first quadrantIn 1st quadrant sin t, cos t arepositive

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A: To show 1-ejα=2 sinα2ejα-π2 , simplify left hand side expression and show equivalent to right hand…

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Q: The values of C, and C2 so that y(x) = C, sin x + C, cos x satisfies the following conditions: y(0)…

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Q: 4. use the Pythagorean Theorem to find the value of cos e. Given sin e %3D 5' A) Cos e %3D B) 3 Cos…

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Q: Show that cos A x e 2 *,x2 0. %3D

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Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

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Q: It is given that sin a + sin b = /5/3 and cos a + cos b = 1. Determine the exact value of cos (a -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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Q: 1+e² sin z + z cos z

A: Introduction :

Q: tan? z sec? x + sec a Prove 1-cos I

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Q: Prove the following Sin? Z + CoS² z = 1

A: To prove that sin^2z+cos^2z=1

Q: Evaluate the following dete sin a cos a sin(a+0)| (a) sin 3 cos ß sin(3+0) sin cos sin(y+0)|

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: If P = A sin 0 + B cos 0 and Q = A cos 0- B sin 0, find the value of A2 + B² in terms of P and Q. А.…

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Q: b. Given that z = el®, show that z" += 2 cos ne. Hence, show that cos 50 = 16 sint 0 – 112 sin² 0 +…

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Q: If sin A = 3/ 4with A in QII, find cos A.

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Q: Prove that the second equality is true and find C and ô in terms of A, B, and w*. ylt) = e alphart(A…

A: The given y-t equation is: y(t)=e-alpha*tAcosω*t+Bsinω*t Now multiply and divide with A2+B2 in…

Q: for which a applies that tan(a) = 2 and that o<a< I. Decide a) sin (a) B) cos(a)

A: Please see the below picture for detailed solution.

Q: T Sin ³ de 3 1-cose

A: I have stated the used formulas in the solution

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Q: 51. Compute x² _ and then using the identity dx in two ways and verify that the answers agree: first…

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

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A: To find: The smallest number x such that cosex+1=0. Concept used: If cosx=0, then x=2n+1π2. The…

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Q: Prove the following identities: sin? 0 - cos? 0 b) tan 0-1=- sin O cos0+ 0 cos²

A: We can prove the following as below.

Q: Compute the indicated quantity using the following data. 15 sin a = where <α<π. 2 3 cos B = - where…

A: We will proceed as follows...