Show using Residue theorem: 1 2πί Is equal to pc+ix c-ix where n = rn sin no (21) 2a (1+2rn cos no + r²n) π |2|= sin po sin 2pa 2a dp kis or 2a = -. n

Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

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Q: Show that T (1-i) cos- +isin- 40 40 (81-8√3) 6 10 = -√2

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Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: Which one of the following is equal to Scot (™) do? 2 ○ 2/4 sec² \sin (12) ○ 2) | + c 2 In sin (18)…

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Q: Sin 0/1 + co² B) 2.

A: sinθ1+cot2θ                             =sinθ1+cos2θsin2θ…

Q: fsin²7x dx Select one: O a. O b. O c. O d. O e. 7x - sin²7x cos 7x 14 7x sin7x cos 7x 7 7x + sin7x…

A: Formula used

Q: If csc e = 1/3t, then where defined, cos 0 A) Square root of (1 – 9t²) 3t/squareroot of (1 – 9t2)…

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Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: (15t-2 – 5t) cos (6t-1+t²)

A: using substitution method to find integration

Q: Evaluate e cosh 2t -3t s13 d) 4(s? - 6s-5) 3. s43 a) 4(s-6s + 5) b) 4(s? + 6s - 5) c) 4(s + 6s +5)

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

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Q: S sec² (7t) tan² (7t) √1 – tan² (7t) dt

A: Given integral:- ∫sec27ttan27t1-tan27tdt

Q: 1-T= 3- Z= +cos(y)tan ( √x-b cos (n) 2-sin²(n) 2-B=sin(x) sec(x)/cscf(x) 4-(w+n)²(a+) x-3

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Q: √ (3(1 + cos 0))² + (−3 sin 0)² do

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Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: b) Prove that, S∞ (@3x+1)² dx e2x 2π 9√3

A: Let we get, Let We get, This implies, This implies

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

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Q: Use complex analysis methods to find T = 6²² 5 I 2π cos 2x 5 + 4 cos x dx.

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Q: Evaluate: fcos In(sin 0 + 4) de O sin In (sin 0 + 4) - 2 cos 0 + 3 ln sin 0 + 4] + C O None of these…

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Q: <{cos 7/½ + j sin 7) 5. Simplify 3. 3.

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Q: d) √3 cos x + sin x = 0 [-2π, 0]

A: By converting the given equation in single trigonometric function,, 99, 254); position: relative;…

Q: Evaluate S dx √x² +25

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Q: 7- The value of (tan³8 + tan³0) e-ten³0 de is. b) 5/2 c) 1/4 0 a) 1/2 d. 5/4

A: The objective is to find the value of ∫0π2(tan3θ+tan5θ)e-tan2θdθ.

Q: a sin(x) -dr. Jr (r² + 1)(x² + 16) R.

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Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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Q: Which of the following represents the fourth roots of (4 – 4/3i) a. -T + 2kt COS -T+ 2kT (8): ( cos…

A: e^(ix)= cosx+isinx  Using that we get the answer.