e). Prove that Sin3A+sinA 25in2A -COSA

Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: Express in the form a + bi where a and b are real numbers.

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

Q: Express in the form a + bi where a and b are real numbers.

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Q: az -? Since it is du coSV.y=. av ) z = In (xry*),x = e"cosv.y= e"sinvr

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Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: points

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Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

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Q: Let the position vcctor bc R CE) = <3€,2 cos (3€), 2 sin (3€) Compute the curuature

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

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: Find the points of intersection between r2 =2 cos20 and r=- %3D 1- cose

A: Find the points of intersection between r2=2cos2θ and r=21-cosθ. for the intersection points both…

Q: if it was fcx) = Sin 3X,9(x)=COS4X EC where the internal multiplication is ove katati ID =S fcx) gx)…

A: f and g are perpendicular when , &lt;f,g&gt; = 0

Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: Let , = cos-+i sin and z, = cos-+isin 6 Express in the form : =a+bi

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Q: Evaluate the principal 5th root of z = 50 (cos150° + j sin150°) and find the absolute value (r).

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Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1+ i).

A: Given: sin2-i cosh1+i To do: Reduce the given into the form a+bi.

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° – sin17°

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

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1 + i).

A: Solution:-

Q: Exercises 1) Find if z = 3 cos x – sin(xy),x = ,y = 3t -

A: The given equation is; z = 3 cosx - sin(xy) , x=1/t , y=3t

Q: Hence prove that sin?a + cos²ɑ = 1 3.2

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: Express in the form a + bi, where a and b are real numbers.

A: 20cos11π6+ i sin11π6

Q: Exercise 2. Solve, for z, the equation Inz = 4 – 3i. Exercise 3. Show that (a) sin z = sin 7: (b)…

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Q: 15. Restate r= 5 cos 0 in rectangular form.

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Q: ,2 - 1 If z = cis 0, show that i tan 0. 22 +1

A: this is complex analysis question and also very lengthy questions so I can do it in advanced…

Q: Prove that there exists a value of x so that -1 COS T = cosx %3D ned to

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Q: Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form…

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Q: Compute | a° sin(æ" + 2) dæ.

A: Given : ∫x6sinx7+2dx

Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

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Q: Prove that: Cos7A+CosA=2Cos4ACos3A

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Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: 5- Prove the following (Answer two only): secA. secB.cscA.cscB a- cos*e – sin*o =cos²0 – sin²e c- =…

A: Answer 2 only.

Q: 71. Use Figure 4 to prove V1- 12 d /1 – x2 + sinx FIGURE 4

A: Let A be a point on a circle of unit radius(r=1) with origin as its center, such that: Calculate…

Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.

Q: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

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Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: 7x sin 4 %3D nswer, including any

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Q: Evaluate the secondary 5th root of z = 50 (cos150° + j sin150°) and simplify to rectangular form O…

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Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: Let fla)= é cosx, s** %3D Express your answers in exact form.

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Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…

Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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Q: Find the length of the path over the given interval. (6 sin(5t), 6 cos(5t)), 0 stsn

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