2- Verify the following identities : [Sinh( u+ v)+ Sinh(u-vl a) Sinhu.Coshv = Coshu.Cosky =- [Cosh(u+v)+ Cosh(u-v)] b) c) Sinh3u= Sinh'u+ 3Coshu.Sinhu=3Sinhu+ 4Sinh' u Cosh'u-Cosh'v d) Sinh'u- Sinh'v

Q: Prove the identitiessinh (x + y) = sinh x cosh y + cosh x sinh y,cosh (x + y) = cosh x cosh y + sinh…

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Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: Find z in 2= Sinh (4-j5). cos (4-5) express in polar porm

A:

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

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

Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

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A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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

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A:

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Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

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Q: using De Moiuve's theor@m, show Tsat sin50 = 16 sino -20 sin o + 5 sin o ニ Hense salve z4 K -30%+ Ex…

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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: Evaluate the integrals

A: Consider the integrals 31)    ∫0π/27costsintdt32)    ∫0π/413tantsec2tdt

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A:

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

A: Given that: y=Acosx+Bsinx

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A: Let's find.

Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: V/ Prove that: (1) tanx= cot

A:

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

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Q: If Y=tanx prove that %3D2

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Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: prove that. sinh ciz) = i sinz sinciz) zisinh z , cescia)= coshz

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Evaluate et sin z cos z dr I COS using Simpson rule with h 20

A: Simpson rule  ∫abf(x)dx=h3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn-3)+2f(xn-2)+4f(xn-1)+f(xn) Where…

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: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

A: The given problem is to prove the following complex hyperbolic trigonometric identity.

Q: 2- Prove that: sin(z + w) = sin z cos w + cos z sin w %3D

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

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: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

Q: 5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

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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: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

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

A:

Q: What is the integrable form of sin-cos-sin0 de 2 2 du 2 1– u² du cosu du -2 sinu du

A: To write the integrable form.

Q: What is the integrable form of sin-cos-sine de? 2 2 (A) - - B -2 sinu du (D cosu du

A:

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

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Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: I* cos z lim 1³+2

A:

Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: What is the integrable form of sin 0 sin-cos-sine d@? 2 2 u² – 1 du 1– u² du 2 | cosu du -2 | sinu…

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Q: Prove the identitiessinh (x + y) = sinh x cosh y + cosh x sinh y,cosh (x + y) = cosh x cosh y + sinh…

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Q: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

A:

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: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.