12 and cot y 13 4 where x and y are in the interval [5, **), If sin x 37 3' evaluate sec( – y). -

Q: f tan x = -5, and cos x > 0, find sec x and cos x 26 26 and cosx = 26 sec x = sec a = 26 and cos x =…

A: Solution-

Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: 41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For…

A: To show the following

Q: 18. Use periodicity to express sec in p given that sin

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Q: Q5. If coshx = csc20, prove that 0 = n+ cothe¯. [Hint: use identity sin(2a + 2n)] %3D

A: given that                                                                             coshx=csc2θ…

Q: + an sin(nx), where aj are real .. + nan| < 1. Problem 88 Let f(x) = al sin(x) + a2 sin(2x) +…

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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: Prove the following inequalities (ii) -10|< sin 0 < |0| and -|0| < 1– cos 0 < |0|

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Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

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Q: he interval [0,2r) cos (x) sin (x) = 2 cos (x)

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Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

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Q: 4. sin 20 + cos 0 = 0 on the interval [0, 27) *Hint: use Double Angle Formula

A: sin(2θ)+cos(θ)=0We know that ,…

Q: Find the two values of 0 in the interval-180° <0<180° such that sin(0) = -0.40. %3D Enter your…

A: Given the trigonometric identitysinθ=−0.40 And θ varies through −180° to 180°

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: 7 Express cach of the followir giving only principal values: (a) sin (2 – i)

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Q: cos プ7 loove -> the on interval the

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Q: 2. The cancellation property sin (sin x) = x is valid for x in the interval Which of the following…

A: (i) Consider the provided information, sin-1sinπ3=π3 Prove that left hand side is equal to right…

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: Let y=f(x)=sin^2(x)-cos(x)+2sin(x)+x find f'(x), factor f'(x) and determine the critcal values on…

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Q: 1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

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Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

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Q: - IF z = tan2 -1 y Show that x- ây

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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: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

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Q: 24. arccsc ( csc D. 8 25. cot(cot-1(-10)) E. 4 rec-(- tan ) 26. sec-1 F. V95

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Q: If sinh x =tan t, 0<t<3/2 , then tanh x = sin t. Select one: O True O False

A: We have been given  sinh x= tan t for 0&lt;t&lt;3/2

Q: Find all points (if any) of horizontal and vertical tangency to the portlon of the curve shown x-…

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Q: HW /Prove that: (1) tanx=cot

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: 6. Suppose that < 0 < n and sin 0 = . Find the other 5 trigonometric functions evaluated at 0.

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Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: For what values of a does f(x) = 2 cos x tangent line? √2 x have a horizontal Give all answers in…

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Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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Q: dr =ズ Sin )=s OP Type a a exact awser Using X as needed

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Q: 4. f(x) = Cos Ex) – 5 Stnh (x) %3D 5. f(x) = Sin(3x)Cos(x) (Hint: use product-to-sum trigonometric…

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Q: Find sin 0 and tan 0 if the terminal side of 0 lies along the line y = 40 in quadrant I. %3D 4/17…

A: Answer

Q: Find the value of s in the interval (0, n/2] that makes the statement true. Round to four decimal…

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Q: Now, let f"(x) =0 and solve for x. Remember that f"(x) = - sin is a periodic function, and thus…

A: use the equation above for solving the equation for x.

Q: If then fyx (1,0) = ? Select one: 0 - sin y -2 None of them 2 f(x, y) = 2x cos y,

A: The required partial derivative is evaluated below.

Q: 17) Prove the following: a) (sin x)(sec x)(cot x) 1

A: Since secx=1cosx  and cotx=cosxsinx Then LHS =  sinxsecxcotx=sinx1cosxcosxsinx

Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

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Q: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

Q: Q1- Show that cote)+tan(e) a. cofe)-tan(9) sec(20) b. sin(36) = 3 sin(@) - 4sin (0) = Se %3D

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Q: that the left hand side of the equation is equivalent to the right hand side. 1- - sin cat Steps:…

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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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