Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

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Q: Evaluate: Jcos 2xdx cos2x cos32х + C 6 A 2 sin2x sin32x + C 6 B 2

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Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: determine the annihilator of the givenfunction F(x) = sin4 x.

A: We have given function; F(x) = sin4 x.

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

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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: Find all values of x in the interval (0, 27] that satisfy the equation sec2 x + 2 cos² x = 3

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Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

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Q: sin xV1 cos xdx

A: ∫sinx1-cosx dxSubstitute t=1-cosxt=1-cosxDifferentiatedt=sinx dx

Q: Verify whether the function g(x) = 1- 2 sin x [1-(π/2)] is the solution of the integra

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Q: Calculate fsin³ a cos° a dx.

A: Let cosx = t Differentiate on both side   - sinx. dx = dt    sinx. dx =  - dt

Q: Exercise(6) Prove that J1/2 = XT sinx 2.

A: Here we have to prove that  J12=2xπsinx

Q: Use the second fundamental theorem calculus along with the chain rule to find sint dt dx sinx 2x…

A: We have to find          ddx∫1xsint dt using the second fundamental theorem calculus along with the…

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: 2. Use the Intermediate Value Theorem to show that the equation sinx = x – 1 has at least one real…

A: In the question it is asked to calculate real solution of equation sinx = x-1. Also, it is asked to…

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

A:

Q: Integrate with respect to x, the square root of (1-cos5x)/2

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Q: Differentiate the function. f(x) = 5 sin2(x) − 8 cos2(x)

A: Given:

Q: Use the Newton-Raphson Method to approximate the root of f(x) = 2 cos(x) – 2x + 1.

A: Newton Raphson method: numarical methods

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

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Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: Find x so that sin 3x + 10 cos x+ %3D

A: Here we have to find the value of x. The solution is following.

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: Find , if da y = 3x cos4x 12x* sin4x – 10x cos4x None -2x4sin4x – 12x° cos4x -12x4 sin4x + 12x°…

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Q: Use the Intermediate Theorem show that there is a root of the given equation: sin a - x between…

A: Intermediate value Theorem states that if f is continuous on the interval (a ,b ) and L is a number…

Q: Find fif f'(0) = 2 sin 0-sec²0

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Q: a3z cos(x – 4y) show that a3z 6. For z = дудхду

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Q: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

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Q: H.co/ prove That;. dz 1-2 Cosh2=

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