5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

A:

Q: 14. Find the smallest positive root of tan x+2 tanh x = 0.

A: Newton Raphson Method:- The root is xi+1 =xi - fxif'xi; i=0, 1, 2, ....   Given equation is tanx +2…

Q: Hiw ABy using Euler's formula prove That : sin(-2)= cosz

A: Euler's formula  Sun(a-b) = sinacosb - cosa sinb

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

A: Use the principal log to find z.

Q: i) Show that the real solution of tanh x = cosechx can be written in the form x = In u + vu. Find an…

A: Note:  As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Prove the identitiessinh (x + y) = sinh x cosh y + cosh x sinh y,cosh (x + y) = cosh x cosh y + sinh…

A:

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: s nip

A: Given z=tanα2

Q: Evaluate the integral: 25 tan² 12x dx Choose the most appropriate answer. tan3 3 12x O 25 × 1 12 ln…

A: Explanation of the answer is as follows

Q: 5 If cosh(2x) = 2 , x < 0 , find the exact value of tanh(x). Enter an integer or a fully reduced…

A: By identity,  cosh(2x) = 2 cosh2(x) - 1  5/4 = 2 cosh2(x) - 1  2 cosh2(x) = 9/4  cosh2(x) = 9/8…

Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

Q: 4. Verify the identity sin(z+y) %3D COB E COS y tan z+ tan y

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

A:

Q: Evaluate the definite integral 3 2 sin (2)dx using Part 1 of the Fundamental Theorem of Calculus. 57…

A:

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

A:

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

A:

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

A:

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

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

Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

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: 10. Integrate the function. 8 ip- 1+ 641 2 sin" 8 2 2 tan- 8 2 tan" 8

A: We have find the integral.

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

A:

Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

A:

Q: Approximate all solutions to tan(x)2 +4 tan(x)– 21=0 in the interval [0°,360°) X = |degrees Round…

A: We have to find

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

A:

Q: Prove that: sinhx + coshx = e* %3D

A: we have  sinh(x)=ex-e-x2cosh(x)=ex+e-x2

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: 19. 2 sin 3x = V2 %3D 21. 2 cos (2x + 1) = 1 23. 2 sin (4x - 1) = 1 3x 25. 2 cos %3D EN =

A: The give trigonometric equation is: 2sin3x=2    ....(1) As we know that if the trigonometric…

Q: 10. Integrate the function. 8 -dt 1+ 64t 2 sin- 8 O A. В. 2 tan- 8 2 tan- 8

A:

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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: Prove using the INT. tan- 1 x = cos- 1 x has a solution.

A: Given:         tan-1x=cos-1x Solve:       tan-1x=cos-1x  ⇒x=costan-1x      ................1

Q: None of These cosh(4t) 7. 2. 7. - sinh( 21) sinh(4t) 7. cosh(21) 7. Sて 1/2 1/2 1/2 1/2

A:

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: 11. True or False. sinh²x = - -+cosh (2x) O a. False. Correct answer is +cosh (4x) O b. False.…

A: topic- trigonometric identities

Q: Prove that : 1. Sinhx= In(x+x² +1)

A:

Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: Lim メーvo s'in 5À sin 3X

A: Given: limx→0sin5xsin3x

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.