33. Use the addition formula to compute cos (4 + 4) exactly.

Q: -)Find the valne of cos 15°. Further s ho w thet Cos 15 <0. Conc lude thut Cos 15° 7 cos 15. (Note…

A:

Q: If z= asen(xy)cos(xy), with a > 0, then the result of simplifying the expression: az əz *əx ây…

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Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

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Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 do. 1+8 cos? 0

A: Note:-  cosθ=eiθ-e-iθ2 Residue Theorem:- ∫Dfz dz =2πi ∑k Res fzk=2πi×sum of residues   Given that…

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A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: 6/155) cos 0, 1+ cos 29

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Q: A-Show that S 1, L{cos at} s2+a²

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

Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: Show that the equation e-2x + 4 cos(13x) = 0 has a unique solution for x E 13

A: The equation is given by: e-2x+4cos13x=0 Solve to get:…

Q: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: 11) (3ysos(3a By cos(3

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Q: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: B Integrate the following. * cos x' dx 2 a.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: 10. Compute the following: »TT/4 (a) COS dx 3 (b) dax

A: Part (a)-Given:

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

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Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: 28- For What Values of a anel k is a X <-1 ー<くく -2 Cx) = ax-b 3 Continuons at every X ?

A:

Q: The value of the integral . rcos ydydr is cos 8 cos 4 b. - cos 8+ cos 4 2 1 c. cos 8 – cos 4 + Cos 8…

A: SOLUTION-

Q: 3. Verify that u = e cos x is a solution of + 8² = 0

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Q: ー19- EX: Fined the sd. of he l-U.2 っ24 ニ4 224 る2 ノ メ424 u())こCos(メ424) + cs(x~て47 ] +出 「d. メー24

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Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: (1) Evaluate the following functions 1. In(3-i6) 3. cos (1+i3) , 2. e(0 52) , 4. tanh (2-i5)

A: As per guidelines, we solve only first question. 1. Given      ln3-i6

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: 3x)=てメ+cosス そし-て)- -4-cosいて) そしね)、ずした) ):-Smいて)=20348 Kntl = Kn - ぐし) 0.9651+2.0 348 32 Satisfied…

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Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

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Q: 9/8 2* CoSメーenp and X=/t+] its dus

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: inside 2 = 2 cos 20 and outside r = 1

A: We have to find area between the polar curve.

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

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

A: Complex integration of the function

Q: Suppose sin(0) = and 0 < 0<T/2. Compute cos(0). (Hint: SOH-CAH-TOA) V3 3 3

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Q: Evaluate the iterated integral. π/4 cos(8) 1¹ Jo 3/² 3r² sin(8) dr de

A: Given: ∫0π4∫0cosθ3r2sinθdrdθ

Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

A:

Q: 22: Evaluate Sea s cos²(y s) ds.

A: Solution:-

Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

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Q: Solve the eaation on the interval. 2sin Đ =3(cos o t D

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Q: solue the following D. E. using undefermind coefficient Method. %3D + COS2 X

A: Solve the differential equation, by using the method of undermined coefficients

Q: Given that cos(2t) = 2 cos (t) – 1, it follows that L{cos"(t)} =;( +:). O True O False

A: We need to find Laplace Transform of f(t) = cos2(t) But , cos2t = 2cos2(t) - 1  ⇒ 2cos2(t) = 1 +…

Q: Express Q(x) = cos4 (x )+ 12 as the composition of three func-tions; that is, identify f, g, and h…

A: Q(x) = cos4 (x )+ 12 We need to express the given function as a composition of three functions  that…

Q: In AXY Z, the mZY = 90°.XY = 19 and XZ = 22. What is cos X? ООО О

A: Given,

Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

Q: QUESTION 11 Use the substitution formula to evaluate the integral. 3n/2 in ede 2+ cos e O In 3 O -In…

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Q: 1 (a) Calculate and fully simplify |a² cos(z) dz.

A: