a) Express 16sin 0 in the form a sin 0 + b sin 30 + c sin 50 , where a, b and c are constant.

Q: Express the number 7√3-3i in the form R(cos(0) + i sin(0)) = Rei, where R> 0 and ≤0 ≤TT. NOTE: Round…

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Q: Find the product of zı and z2 Given zı = 4 (cos 180 ° + i sin 180 °) and Z2 = 4 (cos 145° + i sin…

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Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: Express the number 5√3-3i in the form R(cos(0) + i sin(0)) = Rei, where R> 0 and T ≤ 0 ≤ π. NOTE:…

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Q: * DeMoivre's Theorem 4 (4(os 30 + ) i sin 30

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Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find z5, if z=2(cos π/3 + i sin π/3) and onvert answer into rectangular form.

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are)

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: Show that sin ( 40) (cos 0) (4 sin 0 – 8 sin³ 0). %3D

A: To show: That sin 4θ=cos θ4 sin θ-8sin3θ. Formula used: sin A+B=sin A·cos B+sin B·cos A cos…

Q: Prove that the equation 4 sin 4 has a solution.

A: Given,

Q: Express the number 2√3 – 3i in the form R(cos(0) + i sin(0)) = Reio, - where R> 0 and - ≤0 ≤T. NOTE:…

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Q: let 2=x+iy be a complex number soch that coshe hen Im(tanhe) is equal to sinhycoshy sinh?x+cos²y

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Q: 1) Prove that sin 0 tan 0 + cos 0 = sec 0.

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Q: Find the product of z1 = 2 (cos 213° + i sin 213 °) and Z2 = 4 (cos 33 ° + i sin 33 °) %3D

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Q: tan 6= .and 0s@s90 , then sin 0- O V3 2. V5

A: Solve for sin theta

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

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Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

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Q: V3 Prove that sin 10° sin50° sin 60° sin 70° %3D 16

A: Given, sin10.sin50.sin60.sin70 =sin 60.sin10.sin50.sin70 = [(√3)/2]sin10sin50sin70 =…

Q: Prove that the distance of the roots of the equation sin 0₁ 2³ + sin 0₂2² + sin 031 z + sin 041 = 3…

A: Given equation is  |sinθ1|z3+|sinθ2|z2+|sinθ3|z+|sinθ4|=3 Prove That : The distance of the roots of…

Q: 2) Verify that the equation is an Identity tan 0 %3D sin 0 sec 0 %3D %3D

A: We know that secx is the inverse of cosx and tanx=sinxcosx the objective is to prove the…

Q: Let z=x+iy be a complex number such that coshz #0. Then Re(tanhz) is equal to

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Q: 125 cos – j sin 11 7T 11 1. Simplify . Express answer in rectangular form. 47 + jsin 11 J5 cos 11

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

Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: Prove that X + 8 2 TT sin 8 2 1 sin x X sin?

A: We use Trigonometry identities , double angle formulas to prove this Question

Q: 1 ,3 -r/a0 ? 0 ,² dr sin0d0 ø do = x 32na cos X = ? 0 Jo Jo

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Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.

Q: r=1+Cos ở %3D r = 1- sin 0 2. 0.

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Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: Suppose that sin(θ)=2/6. What sec(θ)=______.

A: As we know that; The trigonometric ratios;…

Q: 2 Convert r = to rectangular form. 7 sin 0 COS

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Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

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: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: 12 (b) sec ( sin 13

A: Evaluate the form.

Q: Q1- Show that cote)+tan(e) a. cofe)-tan(9) sec(20) b. sin(36) = 3 sin(@) - 4sin (0) = Se %3D

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) *

A: I have provided solution in step2.

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

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 sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30°

A: Trignometric ratios are

Q: TT CoS-+COs sin 3 = sin Prove that Sin 3 - 6. 6. 2.

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Q: Prove that; (a) cos4θ- sin4θ = cos 2θ  (b) Sin (π/4 + A) + Sin (π/4 - A) ≡ √2 cos A

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Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

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Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: 7 sin 0 – 1= 5 sin 0

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Q: Express the number 8√3-6i in the form R(cos(0) + i sin(0)) = Re, where R> 0 and -≤ ≤T. NOTE: Round…

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