IRI- 2. <| sinz|< -e 2

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: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: H.co/prove That;- CoS z

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Q: Find Taylor's Sen'ed fey ci) f(x) = sin (2) about x= 1

A: see 2nd step.

Q: b. Prove that 2cot (20) = cot(0) - tan(0)

A: To prove the identity.

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: 103. Prove that for all whole numbers n > 1, sin x = sin (x + d" dx" Hint: Use the identity cos x =…

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Q: Prove that the inequality|cos(x)|≥1−sin2(x) holds true for allx∈R

A: Given inequality is

Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

A:

Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: Q.4// prove that: cothx = In, |x +1 -1 х —1

A: let y=coth-1(x) x=cothy We know that cothy=x=ey+e-yey-e-y xey-xe-y=ey+e-y Multiply ey on both sides…

Q: Prove that 1 < sin x for all x € (0,4). 2

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Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

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Q: Let In = fcos" rdx. Show that: 1 In n n-1 COS x sin x + n-1 -¹ n -In-2, n ≥ 2.

A:

Q: 1 1. Prove the identity cosh2 r = 1 cosh 2x 2

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

Q: 3. Prove that: tan-1z +z %3D

A:

Q: Prove that the inequality                          | cos(x) | ≥ 1 − sin2(x) holds true for all x ∈…

A: we have to prove that the inequality  cos(x)≥1-sin2x holds true for all x ∈R from given , we have…

Q: - IF z = tan2 -1 y Show that x- ây

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: 1. Show that sinz is unbounded on C and lyl <|sinz] <ebl z=x+yi € C. for

A: Given:         We have to show that sinz is unbounded in ℂ and y≤sinz≤ey   for z=x+yi ∈ℂ Function…

Q: Prove that d (sec"x)= 1.

A:

Q: Prove that : <(tan"e) - Ve +1 2e 2 +. Ve? +1 tan

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Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

A:

Q: Here defined the hyberbolie functim diretly in telm of The enponential furictim ;). simh(x) This is…

A: Since you have asked a question with multiple subparts, we will help you with the first three…

Q: Find all values of z such that cosz = 4.

A: We find all values of z such that cos(z)=4

Q: Prove that the inequality | cos(z)| 21- sin"(z) holds true for all z € R

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Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

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: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: 3. ncnt) use PMI to prove that E

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Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: AB is tangent te OC at point A. mod

A: Given : AB is tangent to the circle at the point A. ∠ABC = 37°

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: tan 4X Prove that 4t(1-ビ) if 1-6t +tf t=tan

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Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: show that fE Riemann [o,!] and Find f de

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Q: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

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Q: 3.37 Prove: So" sin" (x) dæ - + 0 as n → oo. (Hint: Use Theorem 3.3.1, but be sure to prove the…

A: Prove that ∫0π4sinnx dx→0 as n→∞. Let fn be the the function defined as fnx=sinnx. The sine function…

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A: