that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: Solve the following DE: (r+sin-cose) dr+r(sin+cose)de=0 O r²+r(sin+cos) = C Or+2r²(sin-cose) = C O…

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Q: Find y" if y= -4 cos x OA. y" 4 cos x

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Q: cos(2A + A) = −3 cos A + 4 cos³ A

A: NOTE: Refresh your page if you can't see any equations. . the left-hand side is  use the formula

Q: 12 A A10. If B then the values of A& B =. %3D (x-2) (x+4) x-2x+4 A 2, – 2 b) -2, – 2 c) 2, 2 d) -2,…

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

Q: Prove that x2 cos x dx = T(2 – n) (+ sin æ)?

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Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: cos t 1-sin t sect + tant

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Q: Perform the following operations: 10. Z = V(100)² + (40)² 11. Z = V(4 x 10-8)² + (50 × 10-9)² 12. Z…

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Q: de -1 < B< 1 (1+B cos 0)² '

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Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: 1 1. Use basic identities to simplify the expression secx cos x + cos x secx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 2) cos² I 6 F/6 sin2 T

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Q: snip

A: sin4θ=sin2θ2=1-cos2θ22=141+cos22θ-2cos2θ=141+1+cos4θ2-2cos2θ=14+1+cos4θ8-12cos2θ=14+18+18cos4θ-12cos…

Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…

A: MULTIPLE QUESTIONS:   “Since you have asked multiple questions, we will solve the first question for…

Q: Evaluate cos x + 2 cos³ x + 1 dx cos' x cos4 x 7 +x + c 2 sin7 x sint x +x + c cos x +x + c 3. cos X…

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Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: QUESTION 2 Je" cos(5x)dx = 7x O A. (7 cos 5x + 5 sin 5x) + C 24 O B. (7 cos 5x – 5 sin 5x) + C 74 e7…

A: Please see the explanation below

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: 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: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

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Q: If cos A + cos B = sin A cos B, then cos(A + B) =

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Q: Compute | cos z dz. cos z +C 3 cos a + sin z +C 3 sin r + cos x +C 3 Cos x - sin I sin z + 5 sin x…

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Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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Q: 1-Cos 2x 1+ Cos 2x ix) tan x=

A: Prove :

Q: d da cos(3) = O-3 sin (3²) O 32.cos(3²) -3.sin(3²).In 3. O sin (3²) O3 cos(32).In 3

A: Given

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: Show that cos + i) =:IG + e) + iv3 - e) 4

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Q: If, Sec t-1/sec t +1 = A-cos t/A+cos t Then A =

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Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

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Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: y = cosx sinx

A: Given query is to the derivative of the expression.

Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: You are given that h (x) C = dh dx for a number c. You have to find c. = 6 sin (7x) + 5 cos(7x) 3…

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Q: Find y" if y = 5x sin x. O A. y" =5 cos x- 10x sin x O B. y"= - 5x sin x OC. y"= - 10 cos x+ 5x sin…

A: Solution: The objective is to find the double derivative of the given function