/Prove that the value of cos()dz, when z = T + 2i is e + e-1

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

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: 7. Prove: sin(t) dt sin(1) + cos(1) 4

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Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

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: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

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

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Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

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Q: 1- d/dz [cosz] = -sin z

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Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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

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Q: Q2- Show that, 2 sin x |Jo(x cos 0) cos 0 d0

A: We have to prove sinxx=∫0π2J0(xcosθ)cosθdθ                     (1) Since we know…

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: Compute 2° sin(x" + 2) dæ. O -7 cos(x" + 2) + C O 1 cos(x² + 2) + C O - cos(2" + 2) +C 1 cos(2" + 2)…

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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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: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: ,2 Compute x² cos(x³ + 3) dx

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Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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

A: Topic:- derivatives

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

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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: Which of the following is true? J sin(3x)sin(4x)dx = cos(x) – cos(7x) dx 2 ® Jsin(3x)cos(4x)dx = […

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Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 1. Evaluate the integral 7/2 cos xesinx *dx

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Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

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

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

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

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Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: Find 2 if x? cos4 cos* T. 1) 2xcos x+4x2cos3xsinx 2) 2xcos x- 4x²cos³xsinx O3) 2xsinx sin xcosx 4)…

A: Hence option (2) is correct.

Q: (b) Prove that 2 -3/2 Js12 (x)dx = sin xy + C. 'COS X x2 x3

A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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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: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: dy.xandy in =cos = COS e

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Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3xbecomes v uz du. -9/29 Select…

A: Given,

Q: H.co/ prove That;. dz 1-2 Cosh2=

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Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

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