Suppose that|x + 4| < 0.024 and |y − 6|< 0.04. Use the triangle inequality to show that |(x + y) − 2|< 0.024 Express 1\2 ln x + 5 ln y − 2 ln z as a single term Simplify the following: sin 3x\sin x −cos 3x\cos x

Q: (a) Apply the Comparison Theorem (Theorem 5 in Section 5.2) to the inequality sin x 0) to prove…

A: Given: Use the inequality  sinx≤x   (valid for all x≥0)To prove:a) 1-x22≤cosx≤1b) x-x36≤sinx≤xc)…

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: 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: 00 How were sin(x) = [° (−1)²₂2k+1₁ -X these values generated from k=0 (2k+1)! (1) (0) n=0 n!

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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: Solve the following: √ ( sin 3x e3x 0 + 2) dx + 2x³ sin 2x) dx 2. 3. f sec x (secx + tanx) dx 7.…

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Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

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. Find the solutions to sin x tan x = sin x on 0<x<360° 6. Find all the solutions to 2cos(2x)–1=0…

A: Use the values of trigonometric values of some pre defined angles.

Q: verify the results  sin 4x = 8 cos3 x sin x − 4 cos x sin x  tan2 x =1−cos 2x/1+cos 2x

A: To prove: sin 4x = 8 cos3 x sin x − 4 cos x sin x Proof: Since sin2x = 2sinxcosx sin2(2x) =…

Q: 1 9. In the proof that (sin-1x) = that sin(sin-1 x) = x. It is also true that sin-(sinx) = x; could…

A: Differentiation of function gives the change of function with respect any variable. The inverse…

Q: use this to evaluate /x*sin (2x)dx

A: Integrating using by parts...

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

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: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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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: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

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

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Q: True or false: If tan 3x = any integer n. + nn for 4 1, then x = %3D

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Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: 4. Show that f(x) = sin(x² + 3x) is equal to g(x) = -x cos(x) at least once on Hint: Think about the…

A: Intermediate Value Theorem (IVT) : It states that if a continuous function f(x) on the interval…

Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

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

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Q: the integral expression on the left to an equal expression on the right. (cos(x)-cos(7x))dx ots…

A: We will solve the integral.

Q: Solve 2cos (x)- sin(x)=2 exactly for all x in the interval [0,27).

A: 2cos2x-sinx=2⇒21-sin2x-sinx=2…

Q: 3. sin(3x) = 3s in x – 4sin³ x

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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: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that          f(x) = x - cosx…

A: As the intermediate value theorem states that if a function is continuous on a closed interval [a,b]…

Q: 1. prove    cos(x)cot(x)= csc(x)-sin(x)   2. prove    cos(x)-sin(2x)/cos(x) = 1-2sin(x)   3. solve…

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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: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: Show me how I can calculate this number easy way Solution ) x(n)= sin(30rnt,) - 2 cos(50rnt,)…

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Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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Q: Solve for the value(s) of x over the interval 0 < x< 360 sin(2) = - V3

A: values=?

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

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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: Using the result of the previous question, explain why 1 n sin" xdx = - sin"-2 xdx. n and hence show…

A: The given problem is to show the result of given integral with using the given integral result.

Q: cos( 2 sin' ( x/ 11)) = Select one: O( 2x2 - 121 )/ 121 O(121 - 2x2 )/ 121 O 22 x/( 121 - x ) O 2x (…

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

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Q: 1. Evaluate the indefinite integral cos x sin³ xdx. 2. a) Evaluate the indefinite integral cos“ xdx.

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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: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: 1- By using simple Iteration method, find one root of the following equation: b- e* * tan x = e-3n/2…

A: The iteration method uses the formula, xn+1=ϕ(xn) to perform the iteration.

Q: #56

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

A: topic- trigonometric identities

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: cos( 2 tan1 (x/ 4)) = Select one: O 2x ( 16 - x2 )0.5 / ( 2x2 - 16 ) O 2x ( 16 - x2 )0.5/ ( 16 - 2x2…

A: Solution:-.