cos (x)+cos(x+x)= 0 = cosʻ (x)+cos(T+x)=0

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

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Q: Solve differential equation  [Sin(xy)+xycos(xy)+2x]dx = [x^2cosxy+2y]dy

A: GIVEN : (sin(x,y)+x y cos(x,y)+2x)dx+(x2cos(x y)+2y)dy=0 let P(x,y)=sin(x,y)+x y cos(x,y)+2x  and…

Q: cos x-2 cos 3x + cos 5x b. cos x +2 cos 3x + cos 5x :-tan x. %3D

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Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

A:

Q: Integrate sin 4x cos 5x + cos 4x sin 5x

A: SinAcosB+cosAsinB=sin(A+B)

Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: 1 -dx cos.x-1 2) Integrate

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Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: Verify the identity.

A: Given: arctanx=12arctan2x1-x2. The interval given is -1&lt;x&lt;1. From the given interval, let…

Q: integral (x 2 + 2x ) cos x dx

A: The given integral is ∫x2+2xcosx dx. It is known that ∫udv=uv-∫vdu. Let u=x2+2x   and  dv=cosxdx.…

Q: 3 cos(x) sin(4x) 3. lim x→0 2x

A: Solution:

Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

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Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 12. etan 2x sec² 2x dx 13. Jdx/(x²-4) 14. (2x¹-x²) dx / (2x² + 1) 15. f (sec²x) dx/(√(1-4 tan² x))…

A: Given

Q: Solve this differential equation. cos⁡x dy+y(sin⁡ x-1 ) dx=0; when x=π,y=-

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Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: secx-1 sin x %3D V secx+1 1+cos x

A: It is basic trigonometry identity

Q: x cos (3x – 7) cos(2x+ 7) lim cos(플-x)

A: Limits

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

A:

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

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Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

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Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

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Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: 9) | sin´x-cos'x dx 10) [ cor"/x - dx

A: Solve: 9)  ∫sin4xcos3xdx10) ∫cot2xxdx

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

A:

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: 2xy cos(x^2) - 2xy + 1]dx + [sin (x^2) - x^2]dy = 0

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

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Q: 1)f(x)=sin³ 2x 2)f(x) = 4coshr 3)f(x) )= sinx cos*x 4)f(x) = e*cosx 5)f(x) = 8 Inx %3D

A: image is attached

Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

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Q: integral cos -1 x dx

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Q: cos 2x - cos2a Integrate cos x-cosa

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Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

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Q: f(x) = VT cos x2 COS 2x f(x) = x² + 4

A: Given functions is, f(x)=xcos(x2) So, differentiating it with respect to x, we get,…

Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: √x(y)²-(√x cos √x - sec √x)y'=1

A:

Q: 5. Using the method of stationary Phase find the leading term behavior of cos (xt*)dt as X 00.

A: To find the leading term behaviour of a function we need to analyze the asymptotic behaviour of the…

Q: V1+ sin (x5) e-y 2(Vx- 1) f-- cos {sin(2x*)} x-2 x2+3x

A:

Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: x*cos (x²) 1 – cos 3x lim X-0

A: we have to find the limit of the given expression