Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

Q: Find y′ if y = tanh−1(sinh x2).

A:

Q: Find cosh 2x sinh? 2x dx.

A:

Q: 2. cos“ y sin’ ydy

A:

Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: 17. sech? x tanhx dx 12

A: Integrated by substitutions

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

A:

Q: sinh In(2+2x) dx? x+1

A:

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A:

Q: Find the indefinite integral. ∫(sec 2x + tan 2x) dx

A:

Q: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

A:

Q: Find the indefinite integral ∫cosh2 (x − 1) sinh(x − 1) dx

A:

Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: 4. f(x) = -sin Зл PS = DCP 11 VS =

A: We have to find the amplitude, phase shift, vertical shift and period of the given function.…

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: if Pen) = Sinh(nw) find F(Z)=?

A: There is an exponential representation of sinhx. Whenever we analyse various properties of sinhx, we…

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: Evaluate the integral.

A:

Q: Find the indefinite integral ∫sinh 6x dx

A:

Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Find the indefinite integral. ∫ sinhx / (1 + sinh2x) dx

A:

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

A:

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

A:

Q: Find the indefinite integral. sinh(4- 5x) dx

A: To find:∫sinh4-5xdx

Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: The given integral is ∫sinh54xcosh4x dx. We have to check whether the given integral can be…

Q: /x[cosh?(2x²) – sinh²(2x²) ]dx is equal to

A: solution :let…

Q: Evaluate ſ tan2 2x sec 2x dx 4

A:

Q: 4 + sinh(3x) = 4 cosh(3x).

A:

Q: Use the hyperbolic identity cosh(2x)= 2 cosh2 (x)-1 to solve 4 cosh(2x)– 22 cosh(x)+ 19 = 0 .

A:

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

A:

Q: (cosh ' []] 1s dz

A:

Q: tanx * In(secx) dx

A:

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

A:

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: sinh 2x cosh 3xdx.

A:

Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: Find the indefinite integral. sec 3x tan 3x dx

A: Given integral, ∫sec53x tan3x dx

Q: What is q'(x) when q(x)=ln((5x^2+x+7)/((x^2/3)(sin(x)))

A:

Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: Evaluate the definite integral. 1 cosh24x sinh 4x dx

A: Note that the following results are to be used for the given question: (i) sinh x=ex-e-x2 (ii) cosh…

Q: S secs/2 (금x) tans (글x) dzx

A:

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,