D[Expl-3x] Cos(nt], {x,2},t]

Q: Integrate -- | cos 5xcos x a) 0.5 b) c) d) 2

A: We can use the trigonometric identity, cos A cos B=12cosA+B+cosA-B . Use the integration formulas,…

Q: find S- とx 1-COS2X

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Q: Q3:- If x= sec 0- cose and y = sec" 8- cos" 0 Prove or disprove that (x2 + 4) ) = n2G2+ 4) %3D

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Q: (b) (cos(x) (2x + 3))'

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Q: - 1, z = cos-

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

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Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

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: 82. Show that cos at cos bt %3D In

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Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: cos 2x +1 Prove that sin 2x

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Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: Evaluate [sin2xcos2x, dx 1 Acos4x+C 1 ® - cos4x+C B 1 -cos4x + C Cos 1 -cos4x + C

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Q: 2dx 2 2 cos x√ 4tanx - tan x S-

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Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

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Q: Therefore, YZ-F Find the coc 1. (-2, 3, 5) an

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

Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: EX/Show that cos"x (1+ cos2x)

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

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Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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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: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: Prove the reduction formula: cos" xdx : 1 -cos"- 1-1 x+ cos"-2 xdx %3D -

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Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: provethat 2. 1- cosx +Sin'x

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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Q: Integrate x3 cos(x4)

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Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

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Q: Find x so that sin 3x + 10 cos x+ %3D

A: Here we have to find the value of x. The solution is following.

Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: Find the positive solution of f = 2x – cosx

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Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

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Q: Prove cos 4x = 8cos'x – 8cos²x +1

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Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: / tan( 4x + 3) dx Evaluate: (A) –In |cos (4x+ 3)|+C 4 B 4 ® -im [sin(4r + 3)| +C В –In |csc…

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Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

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Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D…

A: Integral calculus is the fundamental discovery was the link that exists between this and the…

Q: Prove cos 4x = 8cos*x – 8cos²x+1

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