1 9. In the proof that (sin-1x) = that sin(sin-1 x) = x. It is also true that sin-(sinx) = x; could we have started with that inequality instead? Why or why not? we used the fact dx 1–x²

Q: Suppose that x = cos 0 . Find an expression for sin 0 in terms of a 9 4 z2 6,

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Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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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. Without specifically finding its roots, show that f(x) = 0 for some x E [1, 2] where x2 4 f(x) =…

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

A: Introduction :

Q: 15 and x terminate: 8. Find sin 2x, cos 2x, and tan 2x if tanx = sin 2x |3| cos 2x

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

A: Equation can be solved by taking natural log both sides

Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: b) sin 3x 3 sin x – 4sin3 x [Hint: sin 3x sin(2x + x)] Prove

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

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Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Find the extreme values of the function f(x) = sin(2x) within the interval 0 < x < 2n %3D

A: Given function f(x)= sin(2x)            0≤x≤2π

Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: x* cos 3.xdx 2 fr' cos 3.xdx sin 3xsin 2.xdxr

A: Solving

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: 57 tan 4 177 Determine the value of x if D, sin(7-x)= csc 3 6. where 0sxST.

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

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 2.2 Find all values of x in the interval 0<x< 2n for which -< sin x < 2

A: Given that -12&lt;sin x&lt;12.…

Q: 2. Evaluate the integral (cos (3r)sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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

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

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: 1 Find sin 2.x, cos 2x, and tan 2x if and x terminates in guadrant IV. 10 cosx=

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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: 8 and x terminates in guadrant IV. 15 Find sin 2x, cos 2x, and tan 2x if tanx %3D

A: Given  tanx=-815,  x in quadrant IV

Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: 1 1- (-1)". f (x) = 2 sin nx. - n=1

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Q: Evaluate the definite integral. (1/10 sin-1(5x) dx 1 - 25x2

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Q: 11. y = x² sin x + 2x cos x – 2 sin x 12. y = x² cos x 2x sin x – 2 cos x - -

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Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

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

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Q: 1. Show that | sin x cos3 x dx = sin® x sin x +C = - 8. cos*x, cosx cosx +C 3

A: To prove:-

Q: 278. Suppose that sin(ln x) = 3, and that sin(ln y) = }. If 0 < ln x < and 0 < ln y < , use the…

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Q: (x/2)

A: Please refer to the image below

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

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Q: 4. Find the absolute maximum and minimum values of the function f(x) = cos²x-3 sinx on the interval…

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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: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

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Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…