(1) Evaluate xdx Hint: Express cos* x in terms of sin x. Then use the substitution u = sin x. Back substitute to write your soluton in terms of x solution = + C (2) Evaluate xdx Hint: Use the half-angle identity cos x = + cos 2x) solution = + C

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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: snip

A: Inverse trigonometric function are the inverse function of specially sine ,tangent, secant,…

Q: Use the Intermediate Value Theorem to prove that the equation x² + 2 + 2 COS has a solution on the…

A: Consider the following function: According to the intermediate value theorem: If f is a continuous…

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

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A: Here we have to solve integral question.

Q: Solve the equation below. 3sin x – V3 cos x = 0 if 0 < x < 2n

A: Here given as 3sin x- 3cos x=0

Q: Q3. Use substitution to show that x = n is a solution to the equation sin(x) – cos(x) = 1. Show your…

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Q: sin 2x, Which of the following is equal to sin x cOs x + C 2 sin x + C Option 1 Option 2 sin 2x + C…

A: As we know that the trigonometric identity: sin2x=2sinxcosx And ∫a·fxdx=a∫fxdx Given: I=∫sin2xsinxdx

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A: Given that , Cos(x) = 4/5.  We know that , Sin2(x) + Cos2(x) = 1 Implies , Sin2(x) = 1 - Cos2(x) Or…

Q: fip xp COS T 2. Oa) 2x sin(x) cos(2x) P-sin(2x) d- sin(x)+2x Osin(x) acer

A: y=cos (x2) We need to find dydx

Q: luating√√9-x² dx using trigonometric substitution will lead to: **/2 sin²0d0 3 of th 9[*/ cos²0de…

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A: There may be use of algebra or calculus...

Q: (2) Find the exact value of the following: (i) cos-(-) (ii) tan-V3 (ii) 2tan-1+ tan-1, (iv) sec…

A: (i) cos-1(-1/2) = 2π/3 (ii)tan-1(√3) = π/3

Q: 4. Find the exact value of cos *x- sin "x-cos (2x). 4 cos x- sinx- cos (2x) = (Simplify your…

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Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

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Q: which of the following is equal to į sin x cos (x) dx ? A cos () + C 3. cos (2x) + C O Option 1…

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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: Show use of variable substitution to factor and solve over (0,2pi) when necessary. 2. cos2 θ - cosθ…

A: Substitute x in cos theta and solve the equation.

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: 1+ cos4x A sin4x & 2 2 B cos²2x= 1-…

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Q: Explain why the equation cos x = x has atleast one solution

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Q: 5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) =…

A: Topic = Derivative

Q: Given that sin2   x + cos2  x = 1 and sin x = −√2/5, what is the possible value of cos x

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Q: Find solution of equation 2 o(x) = 2f cos(x-1t) ø(1)dir

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Q: 2 cos' xsin* cos° xsin“ xdx

A: To evaluate:∫0π2cos5xsin4xdx

Q: 8. Simplify: cos(5x) cos(2x) + sin(5x) sin (2x) B) sin (5x) cos (7x) C) sin(3x) D) cos(3x) CoS

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Q: The suitable substitution to evaluate sin24(x+2) dx is None 1 [1- cos4 (r+2)] [1+ cos8(r + 2)]…

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Q: 1 200 -1 1 What is the value of the -coordinate of point A?

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Q: Find the exact value of cosθ. sinθ= -7/25,Pi less than θ less b than 3Pi/2. Cosθ=?

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Q: find exact value 197 8. (a) cos 6 (b) сos 6 (c) cos 6 9. (a) cos 4 (b) cos 4 (c) cos 4 10. (a) sin 4…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: ind sin2x, cos 2x, and tan 2.x if tanx = -2 and x terminates in guadrant II. %3D sin 2x ? cos 2x tan…

A: In second quadrant sin is positive and cos &amp; tan are negative.

Q: 12 Find sin 2x, cos 2x, and tan 2x if sin x=- and x terminates in quadrant IV. 13 sin 2x %3D cos 2x…

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Q: (x/2)

A: Please refer to the image below

Q: 25n B- If cos-1 (cos) = y , Find value of y?

A: B. cos-1cos25π6=y =cos-1cos24+1π6=cos-1cos24π6+π6=cos-1cos4π+π6 cos4π+θ=cosθ =cos-1cosπ6=π6

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Q: 12. sin 2t – tan t = tant cos 2t - HINT: You will use a reciprocal identity.

A: use the formula

Q: If csc(x) = 3, for 90° < x < 180°, then sin() V2 1 V6 2 COS 2 V3+2v2 V6 V 2 - 1 tan 2 V 3 + 2v2

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Q: Show that the equation 2sinx cosx+4cos x=1 may be written in the form of tan x-2 tan x-3=0. Hence,…

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Q: v in the quadrant IV COS (U+V)=

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Q: 2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f)…

A: (a) Consider the given expression: sin-1-1 Sine gives negative one as it value at -π2. Therefore,…

Q: Find sin 2 x, cos 2x, and tan 2xfrom the given information. sinx=8/17, x in QII

A: We have given the value of the  trigonometric ratios of sinx  Sin(x) = 8/17

Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

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Q: The range of this Y= 2 cos (3x) Is?

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Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.