cosh (T– i) = eT cosl - i eT sin 1 + e-" cos 1 + ie- sin 1 - IT 2 e cosl - i eT sin 1 + e" cos 1 + ie- sin 1 et cosl + i e sin 1 - e- cos 1 + i e sin 1 2 e cosl - i e™ sin 1 + e- cos 1 i e- sin 1

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: Exact ODE y'sin2nx-nycos 2rx

A:

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: Find y". y = 6 sin(2x + 10)

A: Given,            y=6sin2x+10

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: S 1 dx = (x² + 1)(1 – sec(tan-1 x)) Select one: а. 1 -x + (sin(cos-1x)) b. 1 -tan(cot-1x) +…

A: Hence option (d) is correct .

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: Evaluate the following integrals -3.r/4 + 8a*]dx -3

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

A: Solution is given: Hope the solution is helpful.

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

A:

Q: Solve csc y dx + sec²x dy = 0 elect one: a 4cosy + 2x - sin2x = c O b. 4cosy + 2x + sin2x = c c.…

A:

Q: Sx-3) (sin (In x) + cos (In x)} dx equals

A: Here we have to evaluate I=∫(x-3)sin-1lnx+cos-1lnxdx

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: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

Q: -4e sin(7y) 4e sin(7y) ду

A:

Q: sec^2 y - tan^2 y = sin^2 y + cos^2 y

A: Consider the trigonometric identities mentioned below.

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: 1-S 1-sinx dx 1-sin?x -sin²x

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: f(seca tan a – 8a")da tan a + a° + c sec a +a8 +e - sec * – a8 +c sec a – a° +e sec a +8

A:

Q: cos° (nt)dt

A:

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: Algebraically prove these formulas are true  r^2=x^2 + y^2 tan theta = y/x

A:

Q: integrate (sin(x)*tan(x)-cos(x))/tan (x+1)

A:

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: coS(T/11)-cos(2t/11)+cos(3t/11)-cos(4Tt/11)+cos(5rt/11)=?

A: To determine the value of the below expression. cosπ11−cos2π11+cos3π11−cos4π11+cos5π11

Q: Using the equation below at angle of 45 degrees, find T^-1

A: Here, the angle is Here, given that,

Q: 4 cos () dx 10. x³ sin3

A:

Q: Y = = ecos(x) + cos(e*)

A:

Q: X₁. (x₁, Yr) (x', y') 0 (x, y) X x' = x + (x-x, )cos-(y-y,)sin y' = y, + (x-x) sin 0+(y-y,) cos P' =…

A: Solution:

Q: Lim メートo Cos aX Cos bX

A:

Q: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: cosh (T– i) = %3D

A: (c) We have to select one option for coshπ-i

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Determine the…

A: We will use concept of arc length in 3d We want to determine the length of a vector function,…

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

A:

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

A:

Q: Sin t/ 1+ cos t = 1-cos t/ sin t

A: The given equation to prove is: sint1+cost=1-costsint Use the trigonometric identity, 1-cos2t=sin2t