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Q: Verify that cos kx is a rolulion Also, stafe what kind of DE is the DE above :

A: This question is about solving differential equations.

Q: Find the Leplace bransform. of Hhe fure tion ESinut octca to biven that

A: Laplace transform of periodic function: The Laplace transform of a periodic function f(t) of period…

Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: -Use Cauchy- Riemman eauadiane to shaw that euch of there tiers is entire. a fizlasxy ti(zy-x) b.…

A: Note: we answer up-to 3 multiple subparts. Please resubmit question which you would like to get…

Q: If acosα+bcosβ+csinγ=0 and asinα+bsinβ+ccosγ=0, then prove that…

A: Given: acosα+bcosβ+csinγ=0 and asinα+bsinβ+ccosγ=0

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

A:

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: 4/ur grans funthon y"-Uy't3y = et

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: a) Show that fi (x) = cos x, f2(x) = cos 2x are orthogonal on [-7, n].

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Prove that, 2cos 2"0 +1 (2 cos 0 – 1)(2 cos 20 – 1)(2cos 2²e – 1...(2cos 2"–19 – 1) 2 cos 0+1

A: Let us take theta=a. So replacing theta with a, We'll multiply both sides by 2cosA + 1 and we'll…

Q: alue of the pur C: |z| = (:-1)(z-

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Q: a) Show that: tan z, + tan z, tan(z, + 2) = 1- (tan z) +(tan z)

A: To prove the formula:

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: af af дх ду af az and of. HINT [See Exam Find 24 fx, у, 2) : x² + y2 + z2 af af ду af az %3D

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Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: 4) Which of the following foumulas does not Kold for all x, we CZ O la wl= |2). Iw). (6) X W = ņ. W.…

A: We know that

Q: 2. (– 13 + 3i)31

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Q: (o, 1,) 1. find th directional denivatve in the dire chons of at 2 Gve inter pretahon of amp uted…

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Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: Queston #o 4 Show that X, Ixe, where x, and Xe E IR X= (1,1,1, -1) Xz = (4,2,2, -1) %3D

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Q: 2.Prove that I (sinwt) : s2+w?

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Q: Let y = sin(sin(50)). Then y" is equal to: %3D Q7 -25 cos (50) sin(cos(50)) – 25 sin(50)…

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Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: IRI- 2. <| sinz|< -e 2

A:

Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

A:

Q: If utt 4ura u(x, 0) = e", u4(x, 0) = 0, u, Ux → 0 as x → ∞, then u e* cosh(2t) O e2 cosh(4t) O e2¤…

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Q: 7) reflection across y =X (х,у)-(у.х)

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Q: -Prove that: y" = 1 if y=csc(tan")

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Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: 123 A=162 3 3 5 9 3 Let Calceelate Ā By Cayley- Hamil ton theorem.

A:

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

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Q: Tofology 2. EX しT X={12/3/4 /5,6 T=Eメ,中っをり,立る, りろ4。 LeT {1,3,4), Topology ? زژه اوم.

A: For the given statement

Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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Q: 12(иxx + uy) %3D3ии. 0 <х< 9, 0 <у<3 и, (0, у, t) %3D 0, и, (х, 0, е) %3D 0, и (х, у, 0) %3D…

A: We are given the following system.       12uxx+uyy=3utt, 0&lt;x&lt;9, 0&lt;y&lt;3…

Q: 2 Verify the identity 4cos x (20 points) 2 2 2 4sin x cos²x + 4sin²x − 4sin³x = 4cos²x.

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Q: 8. Given: ON bisects LJOH, LJ = LH Prove: JN = HN JNH

A: here, in given ∆OJN and ∆OHN ∠JON=∠HON                                      ∵ ON bisect ∠JOH∠J=∠H…

Q: 15. are tag z dr z arc tag z - In /1 + z² + c – In /1 + z² + C %3D

A: By using integration by part

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.