Show that the following statement is true by transforming theleft side into the right side. cos theta tan theta = sin theta

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: az -? Since it is du coSV.y=. av ) z = In (xry*),x = e"cosv.y= e"sinvr

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Q: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

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Q: Tan Be Xe O de d Bo find

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Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: (D² + 2D- 3)y = si %3D

A: Here we use auxlary equation to find complimentary  solution.

Q: To compute sin (3t) cos" (3t) dt, first you need to I Select) * then subsitute u = [ Select ) * and…

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Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

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Q: Evaluate using the substitution u = 1 − x2 or trigonometric substitution.

A: Given: ∫x1-x2dx  ……1

Q: L[cosh(@ot) u(t)], C[sinh(@et) u(t)] and L[cos (@t) u(t)

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Q: dy If tan(ry) + 5 = ry then show that dr? 2y

A: Differentiation two times

Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: Let z x = 2 cos u, and y 3 sin v. Find dz in terms of u and v. %3D Provide your answer below:

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Q: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

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Q: Prove that ∫ cot u du = ln∣sin u∣ + C.

A: Prove that ∫ cot u du = ln∣sin u∣ + C

Q: Let - (sin x cos y, COS I sin y, In). Compute div i

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Q: ha)= Jo So Sin't dt

A: We have to find the given integral .

Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: Give an example to justify that sin (A + B) is not equal to sin A + sin B. Limit A and B to special…

A: Special angles are those angles at which the values of the trigonometric ratios are known. For…

Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: T Use Wallis' formula: sinº (1) cos² (1) dx

A: Follow the procedure given below.

Q: Compute the Jacobian for the substitutions x = ρsinφcosϴ,  y = ρsinφsinϴ,  z = ρcosϴ.

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Q: O sin (z)cos(z)dz

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Q: verify the following trignometric identities. 2cos xsin y = sin (x+y) - sin(x-y)

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Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: Calculate us (t) * sin(t) using the definition of the convolution

A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

Q: find directly the Laplace trans- forms of the functions described (by formula or graph) in Prob-…

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Q: X sin²= cos7 zcos'dx ·COS 2

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Q: Show that if z = cos u + i sin u, then | z | =1

A: We have to show that if z=cos u+i sin u, then z=1. We know for any complex number if z=x+i y then…

Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

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Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

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Q: -4 sin bt

A: Recall:         The First shifting Theorem:               L eat f(t) =F(s-a) ℒsin(bt)  =bs2+b2

Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

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Q: Prove that d/dz sin(z) = cos(z) using Cauchy-Riemann equations

A: Cauchy-Riemann Equation- If f(z)=u(x, y)+i v(x,  y) is analytic, then In particular, These…

Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: Verify the rule by differentiating ∫ du/(a2 + u2) = (1/a) arctan (u/a) + C . Let a &gt; 0.

A: Consider the given integral identity. ∫dua2+u2=1aarctanua+C Differentiate the LHS of the equation…

Q: Evaluate. S cos z In(sec z)dz Your Answer: In(sec z) sin - In tan z + sec + sin z + C

A: Please see the answer below.

Q: If sin-r= In y, show that UTM dy (1-2) = y. dr

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Q: Find cos(u – v) given the following information. 4 sin u = 5' 3 2 1 sin v = 3' 2

A: As per the company guidelines we can solve first question. I hope that the given solution will help…