then If z=e sin 0 = ? О а. 1 O a. 2 Ob. 1 2i +2 OC 2i d. Od. 1 2. +2

Q: ds 53. dt = 8 sin" (+ + 12). s (0) = 8

A: Given : dsdt=8sin2(t+π12)s(0)=8 Solve the initial value problem multiply both sides by dt then…

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: | 12sin z cos zý3 sin? z + e® dz

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Q: 12. Given 0 <0 < 2x, solve 2 cos? 0+3 sin 0 = 3. %3D ○ 등, 똥 ) 플, 풍, 풍 11T ○ 풍,풍 ○ 들, 등, 똥

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Q: A-Show that S 1, L{cos at} s2+a²

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

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Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

A:

Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

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A: In this question, the concept of Z-transform is applied. Z-transform In its most basic form, the…

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Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.…

Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: 2. If 0° < 0 < 90° and cos 0 = ÷, find cos . O 42 V42 V6 6

A: Please see the answer in step 2

Q: اضل وتكامل )2( نظري - طولكرم %3D Question 16 dz sin 1(z) +c dx 6, Not yet answered Select one:…

A: This is false Whose explanation is given below.

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Q: Given that sĩn = %3D 2 |cos 플 호 and COS %3D sin = cos 4 = show without Ee using a calculator that…

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Q: Show that 0 π/2 st sin? xdx TT/2 [ 0 cos? rdr 2

A: A detailed solution is given below.

Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: dy and y= cos't then dx If x= sin?t O -1 O 2 O None of these O -2 1

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Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: Suppose m and n are constants and m‡ n. 1. Evaluate sin(mx) cos(nx) dx

A: using trigonometric identity

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: I don't understand how they got 10 square root of 6?

A: Given,

Q: 13:49 4 Screen. 34 (C) If y = sin 2x + cos 2x , then (y,)o =? ans. none PAE sin+ COs 2

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Q: CT cos 0+r sin 0+5 Evaluate: Si S (r cos 0) r dz dr de O 757/4 O 657/3 O 357/4 О 65л/4

A: Kindly note that there is a misprint in first integration limit .That should be 2 pi. So I have…

Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: du u = ek sin-¹ m. m = sinx.k = 2² Iny,l == then at mv2 In 2 4 In 2 b) 2√2 rv2In 2 # In 2

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Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: 1) Solve det [i4(îĥ.ở)] where ở li ). and în = COS + sin j. (i = V-1)

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Q: for 0 (0° < 0 < 2n) in the equation 2sin e cos e - sin e - 2cos 0 + 1 = 0.

A: Given that, 2sinθcosθ-sinθ-2cosθ+1=0. We know that, sinθ=sinα⇒θ=nπ+-1n+α       α∈-π2,-π2…

Q: 9. 3 cos(wt –@), where w and a are constants.

A: We use first Cos(a-b)=cos(a) cos(b)+sin(a)sin(b) and then we use Laplace transform of…

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Q: 2n e"lao cos² 0 r,? dr sin@d0 $ do = x X = ? 32 παρ

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Q: 2π π14 cosφ SSS p' sinødp døde 0 0 0

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Q: 2 To evaluate the integral (384 + 576 sin(t) + 216 sin (t)) dt, we recall the trigonometric…

A: Here we have to integrate the given Integral.

Q: QUESTION 2 If y-sin-¹ z, show that d'y Hence, deduce that -(1)-(2) - <- 0. dz = M dz dz

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Q: /2 89 cos t 9. dt = 1+ sin?t If q sec e de, then a = b = and g =

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Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: 10. If y = sin 2x + cos 2x, then (yn)o is equal to nn a) (-1)"2" b) 2" c) sin+ cos d) None of these

A: The solution is given as

Q: 29. If H(0) = 0 sin 0, find H'(0) and H" (0).

A: H(θ) = θ sinθ

Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

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Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

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

A: Answer

Q: 1 La So cos " dy dæ COS evaluate

A: We are given the Integral: ∫π2π∫0x21xcosyxdy dx=∫π2π1xsinyx×1x0x2 dx=∫π2π1x2sin xdx It cannot be…

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

A: