Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

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

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

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Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

A:

Q: If e/2i -/2i = sin2 then z = - 2i In(sin2) – 4kn 2i In(sin2)+ 4kT - 2i In(sin2) + 4kTt

A: Given: e-z2i=sin2

Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

A:

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

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

A:

Q: 2. 5. xcos x (sin'x - 2sin'x + sin°x)(cosx)

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Q: 12 If sinh x= find cosh x, tanh x, coth x, sech x, and csch x. 35

A: Given, sinh x = 1235   We have to find  cosh x, tanh x, coth x, sech x  and  csc hx

Q: 15 cos(x) + 4 sec (x)dx

A: 1) I=∫15 cosx+4 sec2xdx =15∫cosx dx+4∫sec2x dx =15 sinx+4 tanx+c   (c- constant if integration)

Q: sin- In?| 4+ tan-!cos- dx 1+ cos2- 4+ tan-cos- 2sin- In2 4+ tan-'cos- dx 2 2 A 1+ cos 4+ tan-'cos- х…

A: Given integral ∫sin x2.ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: Evaluate the integrals in Exercises

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: S 3. sin°ydy 1+ cosy

A:

Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

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Q: (a) Show that cos(x²) > cos x for 0 ;. 1

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Q: sin In 4+tan cos-dx 4+tan-Icos- 2 1+ cos 2sin In4 4+ tan cos- dx A 1+cos 4+ tan-cos- 2sin-In 4+…

A: To rewrite the given integral so that the integral can be evaluated easily. ∫sin…

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: O Lim tanx メーンク メ と5 5+s2 2Lim S+1 ン4 3) Lim 3-→ yリアンチアン49 6+ )Lim I+ Cos メ→

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Q: In(cosh x + sinh x) + In(cosh x – sinh x) = - 1 -1 Leave Question 2.

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Q: O tan-()+ -dx =| Business Mathematics And Statistics x4 +1 Questions 1 O tan-(+e -) + c V2x x2 +1 O…

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Q: Establish each identity given in attachment.

A: To establish the identity: lntanθ=lnsinθ-lncosθ Solution: We know that, tanθ=sinθcosθ Property of…

Q: integral cos^7(4x)

A: To find the integral

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: If y=-cos x, what is x-value between pi and 2 pi corresponding to y-value of 1/2

A: Let's solve  for x value.

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

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Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: $5. (i) show that: sin 0+sin 20 = tan 0 1+cos 0+cos 20 (ii)Find the general solution of the equation…

A:

Q: 9. y = -sin (3x) 10. y = tan (x - 60) 11. y = cos (x + 30) 12. y = 3 cos (2x)

A: In both cases there is translation of graph.

Q: tan" -1 I# Z-X FEMD fyx At (-,1).

A: The solution for the above question is as shown below.

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

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

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Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

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: 3. x² sin* () dx, x² sin2 () dx, n, n, a is a constant

A:

Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: In2| 4+ tan-'cos- dx 2 sin ( 1+cos | 4+ tan-'cos- 2sin- · In²| 4+ tan-'cos- dx 2 (A 1+cos- 4+…

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Q: * /2 2 sinh (sin 0) cos 0 d0

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Q: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: 1+cos 2x dx sin 2z O cot 2x - csc 2x + c O cot 2z +In |sin 2z|+ c O none of these O In (csc 2x + cot…

A: