prove that cosh^2x-sinh^2x=1

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

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Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

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Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

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Q: Prove 9 coshx – 5 sinhx = 15

A: This is hyperbolic function equation so we want to find x value by thi equation so. firstly, we…

Q: Integral of √1-sin2x/2

A: Integral: -The function F(x)is referred to as the anti-derivative or integral of the supplied…

Q: integral of 1/sin3x dx

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Q: Evaluate the indefinite integral: ∫ sec θ tan θ(sec θ − 1) dθ

A: Given: ∫secθ tanθ (secθ-1) dθ

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

Q: Evaluate the indefinite integral: ∫ sec2 x tan4 x dx

A: Evaluate the indefinite integral. ∫sec2xtan4xdx Let tanx=tsec2xdx=dt

Q: Differentiate f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: f(x) = cos(T.x)+ sin(27x).

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Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

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Q: find integral of sin2xln(tanx)

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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: vx +1 Sinh Cschx = In 671 %3D %3D

A: First, let us evaluate sinh-1x.  Let  sinh-1x=zx=sinhz It is known that sinhx=ex-e-x2 Therefore,…

Q: In the indefinite Integral Sin(cosh x + ex). integrand? sinh x + ex cosh x + ex dx, what is the

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Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: On the guide to solve integral sin2x/1+cosx why is the first step changing it to 2cosxsinx/1+cosx?

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Q: */16 etan(1r) sec2(4x) dr

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Q: Show that O tanh(In x) = (cosh x + sinh x)" = cosh nx +sinh nx

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Q: Compute for a real root of 2 cos √x - sin √x = 4 accurate to 4 significant figures using Fixed-Point…

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Q: integral sec2(?) tan2(?) d?

A: Given that sec2?tan2?d?To find : Integral Solution :∫sec2?tan2?d?Let, tan?=tsec2?d?=dt∫t2dtt33+c

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2x = 1.

A: To show that cosh2x - sinh2x =1.

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Give 5 example of Reciprocal rule of Basic Integration Formula.

A: Given: Give examples of the reciprocal rule of the basic integration formula The reciprocal rule for…

Q: Complete the indefinite integral by choosing the correct LETTER from the table: 1 cos(3p) cos(6p) dp…

A: Consider the following formula: 2cosacosb=cosa+b+cosa-b Consider the following integral:…

Q: find the fourier series for the half-Period sine of the function fx) = sinx inthe period 8. xx Then…

A: Given that, f(x)=sinx in the period 0<x<π. ∫n=1∞1(2n-1)2(2n-1)2. The objective is to evaluate…

Q: TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

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

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: 3 26x° + 600 dxr

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Q: a) Use suitable sum and difference identities for hyperbolic functions to show that sinh(5x)…

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Q: Use differentials to approximate √16.5.

A: Given:

Q: solve \int (sin^(5)x)/(cos^(2)x)dx

A: We evaluate  \int (sin^(5)x)/(cos^(2)x)dx

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

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

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

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

A:

Q: compute the integral of    "(sinx * tanhx ) / ln(x+0.01)" from 1 to 5 to at least 6 significant…

A: Given :  ∫15sinxtanhxlog(x+0.01)dx

Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: - Show that sin converges. Hint: Use sinx <x for x 2 0.

A: Given: The series ∑n=1∞sin1n2, To show:  The given series is convergent.

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: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

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Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: 2 cosh x+sinhx

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Q: Integrate sinh2xcosh3xdx

A: Given : ∫sinh2xcosh3xdx

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.