11 a2 uis- こん 3. t cos X = 5 + CoS 20

Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: show that cos 6x = cos 2x (4cos2 2x-3)

A: Given,           To prove: cos 6x = cos 2x (4cos2 2x-3)

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

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: 7T then 6. If 0 = sin(0) = cos(0) = COS %3D

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Q: (sim (6)) 45. y - (1 + uan ()) 6. y = ¿(1 + cos (7)" 43. y sin (cos (2r - 5)) Eises 44. y= cos (5…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Prove cos 4x = 8 cos4x − 8 cos2x + 1.

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Q: [5] Determine the y(2021) of y=cos²

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Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

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Q: Show thatI cos ve (-1/4s)

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Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: Can you show me a step-by-step proof

A: We need the following two identities to produce the required prove:

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

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Q: 16. Evaluate cos(sin¯¹-1) O 0 O ㅠ O 1 O -1

A: Value of Sin(-π/2) is -1

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

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Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

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Q: • If y = cos x2 + x² then • y(5) = 0 TO FO • If y = cos x² + x² then • y(3) = 4x² cos x²2 + 0 FO

A: Explanation of the answer is as follows

Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

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

A:

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: O cos Z 12 15

A: Right angle triangle

Q: Sın 7. os 3x-Cos 72- Sen 3x tan 22 Cos4a+1

A: We use Trigonometry identities  Sin(A+B) = sin(A)cos(B)-cos(A)sin(B) cos(2A) = 2cos2(A)-1 sin(2A)=…

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: 8. Simplify: cos(5x) cos(2x) + sin(5x) sin (2x) B) sin (5x) cos (7x) C) sin(3x) D) cos(3x) CoS

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Q: 7. Suppose x is a number such that cos(x) = sin(x). Then: O a) cos(2x) = cos(x) O b) sin(2x) =…

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Q: 25л then 6. If 0 sin(0) - cos(0) =

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Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

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Q: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: 23-Frove that. Cos3e - Cos'e- 3 Cos e Sin'e

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

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Q: #4 anros y" +47= sin (2x) Hint: you need to modify one time. Long Алаевна

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Q: *7/2 Evaluate sin" x cos x dx for n > 0.

A: ∫0π2sinnxcosxdx Substitute t=sinx Differentiate the above equation dtdx=cosxdt=cosxdx Upper limit at…

Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the…

Q: 40. Show that cos(30) = 4 cos e - 3 cos e for all 0. [Hint: cos(30) = cos(20 + 0).]

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Q: Prove cos 4x = 8 cos4 x - 8 cos2 x +1.

A: In trigonometric ratio,cos2θ=2cos2θ-1

Q: is it right to say cos (60o-30o) = cos60o .cos 30o+ sin60o.sin30o?

A: cos(A-B)=cosA.cosB+sinA.sinB

Q: 5.3 Evaluate (sin (x)cos“(x)dx

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

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de re/2-a (1–cos a). 2

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Q: dx O 32 cos 35 스) -Scos ()+7] + c O 32 cos ()- -cos+c O 32 7 32 CO 5 32 cos 35 (즐) 5sin)+21+C

A: A detailed solution is given below