Show that x² + 1 cos{arctan[sin(arccot x)]} = V x² + 2

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

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Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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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: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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

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Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

Q: [ cos² 2x sin² 2x dx

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: Calculate fsin³ a cos° a dx.

A: Let cosx = t Differentiate on both side   - sinx. dx = dt    sinx. dx =  - dt

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Show that Cosx dx 9- Sin 3D

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Q: Integrate (three) of th 1) f sin6x cos3x dx

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Q: Compute integral sin(cos(x^2)) sin(x^2)x dx

A: Explanation is given below...

Q: Express 2 sinx- v2 cos x in the form of Rsin(x – a), w

A: Given expression is   2 sinx -2 cosx

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

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Q: Compute : exp(i sin(e-i))

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: The value of the integral (x–1)* sin (x 1) (x-1) +cos (x-1) is

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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: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: f(x) = cos (In (3x))

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Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: Find the trigonometric integral ∫cos3( x − 1) dx

A: Find the trigonometric integral ∫cos3( x − 1) dx

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: 2T COs x dx

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Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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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: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

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Q: Show that 4 sin x cos 2x + 3 = 8 cos %3D x.

A: We will use the formula of cos 2x and other formulas of trigonometry to prove left hand side is…

Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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Q: Compute f sin(cos(x²)) sin(x²)x dx

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