Hiw/ If isinh Z= siniz, proveThat: sinhz= sinhxcosy +ising cosh x

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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Q: With mean theorm, show that | cos x - cos y| < ]x – yl for all of x and y at R www.wwwnn

A: Mean Value theorem

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x&gt;0

Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: 1 Proof (I): (sinhx)' = Vx? +1

A: For direct Proof:

Q: zy (Smxa CosX) Axー Sinhy

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Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: 2* csch (2*) cosh(2*)-sinh(2*)

A: We have to find the value of integral

Q: Classify and Solve; +9 = cos² t + sin² t + cosh t + sinh t + 3 sin t – 3t dt dt2

A: d2ydt2+9dydt=cos2t+sin2t+cosht+sinht+3sint-3t…

Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: 3) z = sin(ej³) + sinh(5230°)

A: We have evaluate the given complex number z=sinej3+sinh5∠30°

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

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Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

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Q: I* cos z lim 1³+2

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Q: noitutitaduz ontemonoghtanie sin' x dxsldsinsvlenigito adi to amal cos x

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Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

Q: None of These cosh(4t) 7. 2. 7. - sinh( 21) sinh(4t) 7. cosh(21) 7. Sて 1/2 1/2 1/2 1/2

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Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…