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Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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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: Tan Be Xe O de d Bo find

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Q: show that Itu X tvl = Oe sinu far a sphene of a radus a depined Panamet ui call y by 9 cU,V) =a…

A: Given: Parametric form of a sphere with radius a…

Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: In AXYZ with a right angle at Y, the cosine ratio can be used to find the length of XZ as O a) XY…

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Q: Let the position vcctor bc R CE) = <3€,2 cos (3€), 2 sin (3€) Compute the curuature

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Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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Q: (1+cot 6) de 5. sin' O14 - cote let, u= du=

A: Solved below

Q: i) um asinx-sin2z ,u fünute, fünd the vaue the uimit. tana ofa and

A: Now, the limit is finite given so, the above must be 00form So,  a cos0-2cos0=0⇒a-2=0⇒a=2

Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

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Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

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: Find the crea trom X = 0 to 2 rad y=2 sin '/2 Tr x.

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Q: Find the areg between Ye CosX an d y--SinX trom o tr .

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Q: In A XYZ, ZZ is a right angle and mZX = 53°. Which statement is true O cos 53* YZ %3D XY XZ O tan…

A: From the given figure representative diagram is shown below:   With respect to ∠53°.…

Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Show that a. cosh iu = cos u, b. sinh iu = i sin u.

A: To show that

Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

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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: Y = = ecos(x) + cos(e*)

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

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Q: Done Find sin(20) if sec 0 = 3/2 and tan 0 < 0. %3D 6 Reply 1 Forward

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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: π If the area inside the cardioid r = 8 +8 cos 0 but outside the circle r = 5 cos 0 is A then what…

A: The area is:-

Q: If z = In(x – y) + tan(x+y), show that Z==,

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Q: the exprression csc x/sec x  is equivalent to: 1.  sin x 2. cos x 3. tan x 4. cot x

A: *to find:-  csc x/sec x = ?

Q: Find the conjugate harmonic of v(r,9) = r² cos 20-rcose+2. Show that vis harmonic.

A: Given vr,θ=r2cos2θ-rcosθ+2

Q: tan e lim is 3 5 sin e O a. 1 5 O b. 5 Oc -1 O d. o

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Q: Find the area enclosed by one "leaf" of the three-leaved rose: Bepaal die area wat deur 'n "blaar"…

A: Find the area enclosed by one leaf of r=4cos15θ such that -π30≤θ≤π30

Q: Las longitudes de los lados de un triángulo rectángulo son 5, 12 y 13 como se ve a continuación.…

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Q: why we useltn@) inATOA tor) (sec 1 tan 0 sin 0 cos 0 A(1, 0) Pr FIGURE 2.30 The figure for the proof…

A: We know that  Tan(x) =sin(x)/cos(x)

Q: X sin²= cos7 zcos'dx ·COS 2

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Q: T 2 r = 2 + 4 cos 0 Option 1 r = 2 + 4 sin 0 Option 3 axis? r=2-4 sin 0 Option 2 r=2 sin 30 Option 4

A: Which of the following is not symmetric with respect to the pi/2

Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: { 0, 1, sin’t, cos t, cos 2t } COS a cubcnnco? Juctifu vour

A: This is a question of linear algebra and vector space.

Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: Teorema de residuos: muestre que z=0 es un cero de orden 2 de 1-cos(z)

A: To show that z=0 is the zero of order 2 of the function  fz=1-cosz

Q: Let z = r+iy, r, y E R. Show that if cos a = 0, then cosh y cosh y 1 <1. | cot 2|2 :

A: Let z=x+iy, x,y∈R. Consider cos x=0. And we know that cot z=cos zsin z

Q: sin(x + y) – sin(x – y) = 2 cos x sin y

A: sinx+y-sinx-y=sinx cosy+cosx siny-sinx cosy-cosx siny=sinx cosy+cosx siny-sinx cosy+cosx siny=cosx…

Q: Suppose that sin(In z) = }, and that sin(In y) = }. If 0 < In z < and 0 < In y < §, use the…

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Q: Consider that sin(x) = e, where %3D 0<x< T, then dy tan (x) dx False O TrueO

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