Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

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Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

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A: 5) The given integral is ∫tan7xdx

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Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

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A: To Determine: find the derivative  Given: we have y=secx+tanxsecx-tanx Explanation: we have…

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A: here we have to integrate the given integral.

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A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

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A: Prove that: sinh 2x = 2 sinh x cosh x

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A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

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A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

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A: Differentiate wrt x

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A: we have to find the anti derivative of ∫sinx22xdx...............1 first we put in place of x2 =z…

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

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Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

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A: image is attached

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Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

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A: The given integral is ∫dθsinθ-cosθ

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A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

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A: We use the special results of Gamma function to solve this problem as in next step.

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