TRC Prove that CoshZ =Goshx Cosytrisinh X Siny

Q: sin z In(sec z) dr

A: Answer and explanation is given below.. For 17 and 18 please repost the questions

Q: Show that cosh t + sinht = e and cosht - sinht = e. Hence, show that cosht- sinht=1. Deduce that…

A:

Q: Find the area bounded by the trigonometric curves y=sinx and y=cosx from; x== 3.459 square units…

A: Area bounded by the curve .

Q: tane cote +- = sin0 + cose %3D 9. Sece csce

A:

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

A:

Q: L[sin bd]- show that

A:

Q: find the value of cE CoB] for flx)= that satisfy value theorem. mean

A:

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

A:

Q: sinx dx = Show that 0 sinx COSX 2/2

A:

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: 1/tanx+secx=cosx/sinx+1  verify

A: We simplify the left-hand side first. Multiplying by (secx-tanx) in numerator and denominator.

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

A:

Q: i sinycos ydy

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

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

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

A:

Q: olve the equation on the interval 0s0<2x V2 sin0- sin 0 = 0

A:

Q: x + y ди show that x 1 +-sin 2u = 0 4 If u = cot - x +

A:

Q: integrate sqrt(9* sin^2 (4theta*t) - 1) dt

A: we need to find ∫9sin2(4θt)-1dt Let us take  u=4θt⇒dudt= 4θ⇒dt=du4θ

Q: Find the maximum value of  sinx+cosx at [0,pi]

A:

Q: sine da Seco co?o

A:

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

A: The solution of the problem is given in the next step.

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

A:

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: Integrate cot(x) In(sin(x))dr.

A: The answer is found in step-2

Q: Determine the real root of the equation r sin(x) + cos(x) = 0 in the interval (2, 3) by using…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

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

A:

Q: | cos (5x) cos (3x)dx

A: Given integral: ∫cos5xcos3xdx We know, cosαcosβ=12cosα+β+cosα-β. Also, ∫cosxdx=sinx+c.

Q: Solve part d) only Differentiate Show all work

A: d) y=-12e1x2

Q: Find the equation of the tangent line to the astroid x = cos° (0), y = sin³ (0) at 0 = 5. (Express…

A: The given equation of the astroid:x=cos3θ and y=sin3θWe need to find the tangent line to the astroid…

Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

A:

Q: (sin°x dx

A:

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

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Sinho sechcH) dt

A: To find the integration (sinhx×esechx)/cosh²(x) dx

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

A:

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

A:

Q: Find the product of the integral ri sec²(cos(x))dxdy sin-y

A: Given ∫01∫sin-1yπ2sec2cosxdxdy

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

A:

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

A:

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

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

Q: Differentiate: arctan(cosh(x)) Show all working out.

A: to find the derivative of arctan(cosh(x)) proceed as follows we know that ddxtanx=11+x2  apply chain…

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

A:

Q: Is sinxV9+ cos2 xdx

A: To evaluate the value of given indefinite integral.

Q: sin³ydy 1+cosy

A:

Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

A: