-3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0

Q: nd all values of x in the interval [0, 2x] that satisfy the equation. (Enter your an 9 sin(2x) = 9…

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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,…

Q: Find all values of x in the interval [0, 2π] that satisfy (cos x)2 − 3 sin x − 3 = 0

A: x=3π2 is the only values that satisfy the given condition see the calculation below

Q: Evaluate the integral. π/2 9 sin2(x) cos2(x) dx   0

A: Consider the definite integral: ∫0π29sin2xcos2xdx…

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

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Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

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

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Q: Find all solutions to 2 cos(0) V2 on the interval 0 < 0 < 2A = |

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Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 8. Find all solutions of the equation in the interval [0, 2n) a) sin(x+ t/2) - cos?x = 0

A: The trigonometric equations are:          sinx+π2-cos2x=02cos2x+7sinx=5 The interval for the…

Q: 6. Evaluate A sin³ x cos4 x dx.

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Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

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Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: Assuming In = [ cos" xdx. and n > 2: 1 п -1 n-1 r sin x + -In-2; CoS' In n %3D n

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Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: Evaluate the integral. 7/2 cos 6x dx COS -T/2

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Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: 2. Write –2 cos x – 3 sin x in the form R cos(x – a) with -7 < a < T. Round to three decimal places.

A: Answer is given in asked form.

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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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: 2. Evaluate the definite integral f²n 15 sin*(3x) cos(3x) dx

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.   2 cos x - 1 = 0

A: From the given problem: 2cosx-1=0 Now solve: 2cosx-1=02cosx=1cosx=12cosx=cosπ3

Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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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: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: 1. Evaluate the integral 7/2 cos xesinx *dx

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Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: 7 a Show that for all positive integers n: 27 2n sin nx dx = 0 ii cos nx dx = 0

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Q: 12) f)=sin(x) 0<x<1 Ans. 24 1 (₁ A 7 (1)(3) 1 -cos(2x) +- -cos(4x) (3)(5)

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Q: Find all solutions to 2 cos(0) - V3 on the interval 0 < 0 < 2n -

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Q: 2. Locate the first positive root of f(x) = sinx + cos(1 +x³)- 1 where x is in radians. Use four…

A: (a) We need to find the root between 1 and 3

Q: Prove that 55 sin x² dx - 5 cos x² dx = 1/2 √

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Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: Evaluate D°(cos x +e-2") A cos x – 32e-2x (B) sin x + 64e -2x (c) - sin x – 32e -2r (D - cos x +64e…

A: Here we have to evaluate      D6(cosx+e-2x)

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 8. Evaluate (a). (20-0y di (b). / COS I sin(sin x) dx -3

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Q: 1. Solve cos 2x - 2 sinx - cos*x = -3 on the interval x e [0,21).

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below

Q: 2. Find the solution set on [0, 2n). sin²(x) + cos² (;) – : -2 =0

A: