Which of the following is a solution to the equation 8y' y" + 3 52y = 0 ? а) е t -5t/3 COS b) e-4t/3 cos(2t) O c) sin(t) e-t/3 cos(4t)

Q: )3--find all solutions of the equation 2sin? c-cosx=1 in the interval [o, 27).

A: To solve the following trigonometric equation  2sin2x - cosx = 1

Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

A:

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

A:

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: 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: Show that 0=30° is a solution to (sin 0)sine 4. 1 5/-

A:

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

A:

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 2. Solve: sin 3x dr + 2y cos 3x dy = 0

A:

Q: x³y"+xy'+4y = cos (2 In x)

A:

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: Approximate all solutions to 8.cos(x)2 –6.cos(x)+1 in the interval [0°,360°) X= degrees Round your…

A: The given equation is quadratic in cosx.

Q: Solve che DE'sin with Euler 2?

A: For the solution follow the next steps.

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

A:

Q: Find all solutions of the equation in the interval [0,2π) cos3xcosx+sin3xsinx=0

A:

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

A:

Q: dt cos (2 sin 21) /1– 4r

A:

Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

A:

Q: (2.) (1-(In))^ (3.) yn + sin ()

A:

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

A:

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

A:

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: Solve for 0: 2 cos (0 –) - -) = - 1, where O" <0< 2n".

A:

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

A:

Q: 27 Show that the equation cos? x – 3 sinx cosx +1=0has only four solutions in the interval (0; 2pi)

A: Solution is here

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: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

A:

Q: Find the equation of a cosine wave that is obtained by shifting the graph of y = cos x to the left 7…

A: We have to find the equation of a cosine wave that is obtained by shifting the graph of y = cosx to…

Q: d. Show that sin 8x + sin 4x cos8x-cos4x = -cot(2x)

A:

Q: Solve for all solutions to sin3xcos2x + cos3xsin2x = 1 [0, 2pi] on

A:

Q: Cos2x dx (1-sin2x)4

A:

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

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

A:

Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

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: Exercises To Solve [No.5] 6 "Cosx dx. Sin²x+25inx+5

A: Here is the solution

Q: Find the general solution 6. y"+4y' = sec2x Solution 6. y=c, +c, cos 2x+c, sin 2x+ 16 sin 2x -In(sec…

A: Given differential equation is y'''+4y'=sec2x We have to find the solution of the given differential…

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

A:

Q: e). Prove that Sin3A+sinA 25in2A -COSA

A:

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

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

A: SOLUTION-

Q: b) Use the hyperbolic identity cosh(2x) = 2 cosh? (x)–1 to solve 4 cosh(2x)- 22 cosh(x)+19 = 0.

A:

Q: The suitable substitution to evaluate | sin 4(x+2) dx is None (1- cos8(x +2)] [1- cos4(x + 2)]…

A: Given that: ∫sin24(x+2)dx

Q: Find sin 2x, cos 2x, and tan 2x if sinx= and x terminates in guadrant IV. sin 2x %3D cos 2x %3D tan…

A:

Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b

Q: Which of the following is equivalent to cos (60° + 0) + sin(30° + 0)? cos 0 + v3 stn e cos e O…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.