i) L {8e")=? ii) L{2cos3t}=? iii) L {e²*sin4t}=?

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A: In the question we have to prove the given function.

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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

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A: Simplify the given expression: Coshπ-i

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

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Q: 9) -135° Pos Neg Sin Cos -:-

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A: We have to determine the integral

Q: 43. If > 2, then -dr = - 4 Jcos (4) + k B sin- ()+ k '(;) + A Cosh- (5) + k cosh=(4 D 2 tanh-(4) +k

A: for this integration, we will assume that x=sec(theta) and from that, we will solve the integration.…

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

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A: We will use L'Hopital rule

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A: In this question we have to find solution by using Integration by parts.

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A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

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Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

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Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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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

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A: Given: cosh(sinh(lnx))=x2-12x. The objective is to verify the left hand side expression.

Q: *(+²–1) cos[cosh (In r")]dr 4.

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Q: Suppose, z=-i+1.7 then, Find e-iz e(cos 1.7 +i sin 1.7) e(cos 1.7 - i sin 1.7) (cos 1.7 - i sin 1.7)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

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Q: Please I want solution of question 8 with step by step. Many Thanks

A:

Q: 7. Evaluate Arc cos(j2).

A: It is principal value.

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

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A: We have evaluate the given complex number z=sinej3+sinh5∠30°

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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: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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A: If n is odd use substitution with u=sin x, du=cos xdx and convert the remaining factors of…

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Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: 2 = sin5t constitute a fundamenta L

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A: topic - definite integral

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Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt