be (a) sin-z= linz+c (b) sinh2= lnr+c (c) cosh = Inr+c (d) tan-= 1In r+c (e) None of the above 21

Q: 2. LOshx-Sin hx1 2. Co

A: We use hyperbolic Trigonometry identies

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

A:

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: 9. Sin 2X dx COS 2X

A:

Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

A:

Q: 5 cos2(x) sin(2x) dx

A:

Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: 15. cos³ 3x 3√√/sin 3x dx

A:

Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: Find sin 4.x cos 8x dx.

A:

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

A:

Q: what is the acceleration at time t=o of a particle if its position is s(t)= cos (3t)-sin(4t

A:

Q: Find ∫sin3 x cos4 x dx.

A:

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 4 sin 6x cos 3x dx 1. %3D - 9.

A:

Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

A:

Q: /2 Evaluate sin 20 de sin20 x+ cos x 20

A:

Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

A:

Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

A:

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: 4 cos () dx 10. x³ sin3

A:

Q: find | cos*x dx 1 1 1 А) — — х —- sin2x + —x + — sin4x + c 4 1 B) =-x +- sin2x + X 4 1 8 1 x + sin4x…

A:

Q: 2. Find a reduction formula for sin" x dx. By using this formula evaluate sin® x dx.

A: The objective of the question is determine the integral.

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: sin(6x) cos(4x)dx% = %3D (b) ÷( + ) Nin (6x) cos (2x) COR +c 2. 2)+ (e) None Cos (2x) Cos (10x sin…

A:

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 7. Find the derivative with respect to x of tan-(2) – In(2.r +3) = 4 cos (2y +5). %3D

A: To find the derivative of tan-1x2-ln2x+3=4cos32y+5. Solution: Power rule of differentiation states…

Q: 4 sin' 2x cos 4x dx 4.

A:

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x +2 = 0. b. Express tanh x in terms of e*…

A:

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: ating / * sin (2x)cos(2x) dr by substitution, if u= sin(2x) th

A:

Q: If e/½i =sin2 then z = - 2i In(sin2) + 4k TI 2i In(sin2) + 4k T - 2i In(sin2) – 4kT -2 In(sin2) + 4k…

A: We will find the solution

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: 8 sin(2x) cos(2x) dx

A: We have to evaluate the given integral

Q: За (cos 4x sin 3x – sin3 x)dx a

A: Given: I=∫a3asin3xcos4x-sin3xdx We know that sinAcosB=sinA+B+sinA-B2…

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

A:

Q: v² operates on sin(-3x) + cos(3y)

A:

Q: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.