(6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

A:

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

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Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: What is the formula for integrating sin 40 cos 20d0 ? S (sin 60 – sin 20) do S (sin 60 + sin 20) de…

A: SOLUTION-

Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand?…

A:

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: 4. Evaluate sin (44°) + COS (290) using differentials. Refer to special triangles.

A: To evaluate  sin440+cos290 using differentials.

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2 9) -sinh? -cosh -dz

A:

Q: 1 L-1 s(s² + 4). 1 1 [1+ sin(2t)] 2 [1 – cos(2t)] | Option 1 O Option 1 1 1 [1+ cos(2t)] 4 [1 –…

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Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: 8 Find L-- 8s2+6 sin Vt cos Vt COS V V등 sin y응t COS

A:

Q: establish each identity.

A: Given  The identity is ln sec θ=-ln cos θ

Q: 9) -135° Pos Neg Sin Cos -:-

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Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

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Q: The value of integral (cos(4x)+cos(81)) dx

A: We have to determine the integral

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: Flnd * |(sin 5x cos 3x + cos 5x sin 3x) dx cos 8x cos 3x + 3 cos5x – + c 8 + c Option 3 Option 2 cos…

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Q: In(1+ Vsin²x) lima→0 1 – cos x

A: Given,limx→0ln1+sin2x31-cosx

Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: 25. y = 2 cos yA 2 28. y = 2 sin ) -2TT -2 31. y = 3 sin (2x) (A)

A: In this, the amplitude is multiplied by 2 and x is scaled by 1/2.

Q: 4. Evaluate et cos xdx.

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

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Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

A:

Q: 5. If cosh 2x then the positive value of 4 sinh 2r is

A: Here we will use the relationship betweencosh2x and sinh2x to find the value of sinh2x from the…

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

A:

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

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

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Q: i) L-- (In) L- | s-3 6s+3 ii) L-1 iii) L(tet cos wt) s+1 sª+5s2+4,

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

A:

Q: 3. In (cose) tane de

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Q: z sin(2- 32)+cos(2 - 3a)+c | 4x cos(2 – 3x) dx 4x cos(3 3r) dx Option 1 Option 2 |4 cos(3- 3z) dr…

A:

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: 22 Evaluate s cos (Iz)e dz

A: Formulae used: ddxcosx=-sinxddxsinx=cosx∫eaxdx=eaxa∫cosxdx=sinx+C By party integration formula…

Q: 8. 4 6° sin°3ycos *3y dy

A:

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

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

Q: If fex) cos cmx) dx = and %3D fox) E Coscn'x) then %3D COS n3 +! KIN

A:

Q: 3) If y = sin(2n), and x = cos(2n)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: I have a question about this type of question. Will cos(mpix) will always be 0? and how do we…

A:

Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

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

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.