Prove that (csc(x)) = -csc(x) cot(x). 1 d -(csc(x)) dx sin?(x) sin?(x) 1 sin(x) sin(x) = -csc(x) cot(x)

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A: Indefinite integral: - The term "indefinite integral" refers to an integral that has no upper or…

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A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

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Q: 4 cos 4 cos dx () х3 sin3 4 - у4 - х dx

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Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

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Q: Verify the identity: (sin x - sin y)/(cos x - cos y) = -cot (x+y)/2

A: sinx-sinycosx-cosy=2cosx+y2sinx-y2-2sinx+y2sinx-y2=-cosx+y2sinx+y2=-cotx+y2…

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A: as per the company guidelines, I can solve only one question.

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

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Q: tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

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Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

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Q: Prove that (csc(x)) = -csc(x) cot(x). dx 1 d -(csc(x)) d dx )(0) – - 1 sin2(x) sin?(x) 1 sin(x)…

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Q: sin x (cos x + 4) dx 1+cos²x

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Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: | sin(4x + 3)cos(3x – 5)dx -

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Q: sin x (1- cosx) dx (1– cos² x)

A: To evaluate the integral: ∫sinx1-cosx1-cos2xdx Solution: Evaluating the given integral:…

Q: )Find the anti derivative for sin(x^2) 2x

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A: (NOTE- Since it seems to be a typo mistake so, assuming that in the given integral all the variables…

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Q: . Evaluate cos 3x sin² 3x dx

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Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

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Q: Evaluate (sin² (sin² x cos x)(1+ sin z cos x) dx.

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Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x