4s – 20 s2 – 4 Select one: None of these O 4 cos 2t – 10 sin 2t O -3e2' + 7e-21 O 4 cos 2t + 10 sin 2t O 7e?" – 3e-21

Q: {; S s2 – 4s + 13 Select one: (cos cos 31 + sin 3t ) O (cos 21 + sin 21 ) 3 -sin 2t 2 -2t ( cos 3t –…

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Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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Q: 2 += cos 3t 3 -- sin 3t 4 3. L 20s? – 103s + 423 6. 28(s – 5)(s? – 9) 20s? – 103s – 423 20s2 + 103s…

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Q: 19. Evaluate the following sin³ [sin³ (2) cos(4) dx 32 A. 35 COS 5( 4 ) [-5cos² (4)+7] -cos 32 32 -…

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Q: 3. * S cos(3z)sin1º(3z) dz A 1 C (sin(3z))10 + C 3 (cos (3z))10 + C - -- В 1 (cos (3z))'1 + C 33 1…

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Q: 3. у %3D In(5 — е**) 4. x = et (cos 2t + 2 sin 2t)

A: Now the first given function is ln5-e4x The second given function is x=etcos2t+2sin2t To find the…

Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: (종-272 27=) + ain G + 272) The simplified form of cos O V3 cos 27z + sin 27z V3 cos 27z + v2 sin 27z…

A: Given cosπ6-27x+sin(π3+27x)

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: 1 L-1 s(s² + 4). 1 1 [1+ sin(2t)] 2 [1 – cos(2t)] | Option 1 O Option 1 1 1 [1+ cos(2t)] 4 [1 –…

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Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

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Q: 14. If we let u = 4x – 1 for the (2tan(4x-1)-3 cos“(4x=1) dx. what will be the cos(4x-1) resulting…

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Q: Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4…

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Q: Find L {(2- t) (5 cos 3t 1)}. - 5(s²+9) (s² –9)² 10s - 82-9 5(s2-9) 10s - - s2 s2+9 (s²+9)² 10 82…

A: As we know from the Laplace transformation; 1). La·ft+b·gt=a·Lft+b·Lgt 2). Ltnft=-1ndndsnLft And…

Q: Find L{(2-t) (5 cos 3t – 1)}. 10 s3 s2 s2-9 s(s² –9) 10s 5(s+9) 1 s2 s29 (s²–9)? 10s 5(–9) $29 (2+9)…

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Q: 43. If > 2, then -dr = - 4 Jcos (4) + k B sin- ()+ k '(;) + A Cosh- (5) + k cosh=(4 D 2 tanh-(4) +k

A: for this integration, we will assume that x=sec(theta) and from that, we will solve the integration.…

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: L-' ( In 8s4 (252+25)(4s²+16) 2 cos 21+2 cos( 1)-를 2t cos 2t + 2t cos ( 1) - 2 cos 2t+2 cos :)- cos…

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Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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Q: -24-4s e S COS os(28) – 7 sen(28) cos s+6 s2 + 49

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Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: 1. Determine the value of cos(2x+2y) if sin z 3 and tan y = - for 4 sysa. for 0sxs: VI VI

A: Given : sin x = 3/5 and tan y = -3/4

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

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Q: sin(k/n). 1. cos(1) + 5/3. 2. cos(1) + 1/3. 3. cos(1) + 2/3 4. cos(1) – 1/3. O 1 O 2 O 4

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Q: 1) z = 6| cos 3T +i sin 2 +i sin 6 W = 12] COS 6 Find 2.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: 3 Show that sin' 0 cos“ 0 1 1 cos (40) + 32 cos 128 cos ( 80). 128

A: To prove that,           sin4θcos4θ=3128-132cos4θ+1128cos8θ

Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: Find L{10) } s(s²+16) 1+cos(4t) 16 1-cos(4t) 4. 1-cos(4t) 16 1+sin(4t) 4 1-sin(4t) 16

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Q: (sin 4z + cos 4) O 2+ sin 4I COs 4r O 1+2 sin 4x cos 4x O 4+ sin 4I COs 4x O 1+2 tan 4x cos 4x O 1-…

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Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: L= {4 sin (3t) + 2 cos (9t)} L = {sin (2t) cos (2t)} 4s 6 2 + s2+1 s2 –9 s2+4 4s 6 + 82+1 2 s2+9…

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Q: Graph the functions in Exercises 13–20. What is the period of each function?

A: Dear student, Since you have posted multiple questions, as per our policy we will answer first…

Q: sec 0 + In + 22+3 = -3 2 In y + 322-4 = 1+ cos 20 2/1+ (tan 0)2 +2ln y+2 3

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Q: ſcos15x cos4x dx * 1/2 (1/11 sin11x +1/19 sin19x )+ C O 1/2 (1/11 sin11x) + 1/19 sin19x + C None of…

A: Solution

Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A: Given: cos3y+sin2x=2x+3y To find dydx in the given equation.

Q: 54 L-1 ( In (s² +25)(s²+16) cos 5t-cos 4t + 2 cos 5t – 2 sin 4t - 2 - cos 4t – sin 5t 2 sin 4t-cos…

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Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: 4. 4sin(x)cos(x)+2 cos(x)-2 sin(x)-1=0 -13D0

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Q: The simplified form of cos ( - 12a) + sin (* + - 12=) 6 O v2 cos 12r + 2 sin 12x O V3 cos 12a + v2…

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Q: 2 tan(4x-1)–3 cos²(4x-1) dy cos(4x-1) 4. If we let u = 4x -1 for the ', what's going to be the…

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Q: The simplified form of cos G- 13x) + sin + 13x V2 cos 13z + 2 sin 13æ O v3 cos 13z + sin 13x O cos…

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Q: 3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t +…

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Q: Find L-1 s2+4s+29 cos(5t) -cos(5t) O 15 cos(5t) – 2 sin(5t)] - O sin(5t)

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Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: 5. Evaluate SO-2²πT ydx = 3π₁ given x = 0 - sine, y = 1- cos -0

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Q: 14. If we let u = 4x – 1 for the s²tan(4x-1)-3 cos"(4x-1) dx. what will be the cos(4x-1) resulting…

A: This is a integration problem