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

Q: (с) 4у" + у %3D 4 sin(3x/2), for 0 <x <л, У (0) %3 0, у(л) — 0

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Q: snip

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Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

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Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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

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Q: sec(θ)=11/3

A: Please refer to the image below

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: 11m If 0 = 6. then sin(0) • %3D cos(0) =

A: Answer

Q: S Show that L(cos² 3t – sin² 3t)= 82+36

A: Using Laplace transform,

Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: 57 where 2 tan 0 = <0 < 3T 3 Find sin 20 7 24 24 25 24 25 25 24 4,

A: By using sin(2x) formula in terms of tan(x).

Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

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Q: S sin° (3t) cos(3t)dt Evaluate COS

A: To determine the value of the integral.

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: 9 If f(0) = cos 0 · cos 02 cos 03 ....... cos 0n %3D f'() + tan 0,}=- f (8)] Show, {tan 0, + tan 02…

A: Introduction :

Q: 2 Z = 31 + (Sin 28 + ((ase Ÿ -(Sin@) Fined Iz1 12

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Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: Find sin2x, cos2x, and tan 2x if cosx - and x terminates in guadrant III. 13 sin 2x cos 2x tan 2x

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Q: 8 and x terminates in guadrant III. 15 Find sin 2x, cos 2x, and tan 2x if tanx= sin 2x %3D cos 2x…

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: S(2) = vāsin(5z) sin z

A: Differentiate w. r.t to x

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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Q: 15 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in guadrant III. 17

A: Given that: sinx=−1517 To find: sin2x, cos2x, tan2x

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: 1 Find sin 2.x, cos 2x, and tan 2x if and x terminates in guadrant IV. 10 cosx=

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Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

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: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: 5. Evaluate 1. S, sin(x2) dx

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Q: 22 Evaluate s cos (Iz)e dz

A: Formulae used: ddxcosx=-sinxddxsinx=cosx∫eaxdx=eaxa∫cosxdx=sinx+C By party integration formula…

Q: 21) (1 + cos 9t) 2 sin 9t dt

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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: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

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: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant III. V13

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Q: sec 0 + In + 27+3 = -3 2 In y? + 327 – 4 = 1+ cos 20 2/1+ (tan 0)² + 2ln /y + 22 = -3

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Q: Find sin 2x, cos 2x, and tan 2x if tanx=-. and x terminates in guadrant IV 3

A: sin 2x= 2 sin x cos x cos 2x=1-2sin2x tan 2x=(sin 2x)/(cos 2x)

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

A:

Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt