5. Simplify the following expression! (1+2i)|3+ i[² (c +i· sin 6. COS |

Q: Q1: Solve the following O.D.E у"- Зу'- 4у%3DЗе + 2 sin x - 8e* cos 2.x.

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

Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: Verify the identity. 4 cos(sin-1 x) = V 16 – 16x? Let e = sin-1 x = sin e = x = X. * Thus, 4…

A: Explanation of the answer is as follows

Q: s nip

A: Given: 12cos2x+C=14cos2x

Q: What is the value of O (less than 2n) that will satisfy the following equation? sin 20 +4sinO + 3 =…

A: We factored the given equation and solve it.

Q: 4. Solve the following equations on the interval 0 < 0 < 27 3 cos 0 + 3 = 2 sin² 0 а. b. sin (20) +…

A: As given expressions and intervals is 0≤θ&lt;2π a)  3cosθ+3=2sin2θ 3cosθ+3-2sin2θ=0 Consider…

Q: 13. What is the correct equation to solve for x? 13 45 O a) tan (45) = x/13 O b) cos (45) = x/13 O…

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: "/4 4 12. r² sin 0 cos 0 drd0 0 0

A:

Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

A: Here I am attaching image so that you understand each and every step.

Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: 7. The value of A. cosx - C O A O B О с O D dx √(1-x is B. sin '(x)+c C. cosx ' +2¢ D. cosx

A:

Q: 7. The value of 2 cos (sin-1 (-0.6)) is: C. 0.8 D. -0.8 A. 1.6 B. -1.6

A: To find: The value of 2cossin-1-0.6. Formula used: cos-x=cos x Inverse trigonometry relation;…

Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

A:

Q: /2 S cos (x) sin (æ) da = COS 0. 6. 15 15 O None O 15 2 45 2

A:

Q: 9) 5olve For OLO<2M Cose+sin A =1 2.

A:

Q: 4. Evaluate y = sin¬1 (x) when x = 1 %3D O 37 2 -1

A:

Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

A:

Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &amp;…

A:

Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

A:

Q: 8 r = 1 + 4 cos(0) e = |4

A:

Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

A:

Q: 1. Convert the following expressions to its Julia equivalent. x+y² √√π-25) (a) e - cos' (2) sin³²…

A: We have to convert given expression to Julia equivalent. In Julia we have: a^b as ab exp(a) as ea…

Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx-

A: To evaluate we first multiply and divide by 2 the given function.  Then use the formula: 2(sin(mx)…

Q: 22. If y = (1- sin?x)i then y" is b. 1 COS X 2° а. C. - cos x d. -sin x sin x HIN HIN

A: The second derivative of the given function is solved in detail below.

Q: 4. Evaluate the following in terms of Gamma function sin (4r) cos (2r)dr

A:

Q: (1) Evaluate the following functions 1. In(3-i6) 3. cos (1+i3) , 2. e(0 52) , 4. tanh (2-i5)

A: As per guidelines, we solve only first question. 1. Given      ln3-i6

Q: Find: L [sin 2 5t ]. 0-co 5 Cos 10t) s² + 25 O A.) B.) 1 5 s² +25 2s 2(s +100) C.) D.)

A:

Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: Solve the following over the interval [0, 27]; Sin 2x Cos *- Sin x = 0 O 0, 0, 6 O 0, 7, 2m, , O 0,…

A: Given sin2xcosx-sinx=0 The trigonometric identity used is sin2x=2sinxcosx So the expression becomes…

Q: How many values of 0 in the interval 0 < 0 < 2T satisfy 1 – 3 sin 0 + 5 cos 30 = 0? %3D (A) 2 (B) 4…

A: The aim is to determine the number of values of θ in the interval 0≤θ≤2π satisfies 1-3sinθ+5cos3θ=0.…

Q: T/3 4 sin x 1- So" 1-4cosx

A:

Q: 2 7 sin a da 1+ cos z

A:

Q: (2) Solve the following equations for x giving all solutions in the domain. (a) 2 sin(x) − 1 = 0, x…

A:

Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

A:

Q: Q1:- Solve the following DEs:- xy2-cos x sin x 1) y' = y(1-x²)

A: The most general form of a linear differential equation of first order is dydx+Py=Q where P and Q…

Q: 1o² (sin x + cos x)dx = O 2 O None O 1

A:

Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: Given x[n] = x1[n] + x2[n] where, Ttn x1 [n] = 9 cos and x2[n] = 8 sin 4 8

A: Given: xn=x1n+x2n x1n=9cosnπ4 x2n=8sinnπ8 To do: Graph x1n using Scilab.

Q: 2. Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5* (B cos 2x + C…

A:

Q: 12. If f(x)=sin(2x+1), then f'(x) is equal to A -2 cos (2x+1). 2 cos(2.x+1). 4 cos(2x+1). C D -4 cos…

A:

Q: 19. Given 0 <0 < 2T, solve 2 cos² 0 +3 sin 0 = 3. ○ 등, 똥 6 6 ○ , 풍,풍 ○ , 풍, 똥 5w 6 ○ 풍, 풍 11.

A:

Q: Solve the following equations for x over the interval [0, 2n). 1. 2 cosx+4= 5

A:

Q: 10. If y = sin 2x + cos 2x, then (yn)o is equal to nn a) (-1)"2" b) 2" c) sin+ cos d) None of these

A: The solution is given as

Q: Solve for O on Co, 2T) 6 sinio + 9 cos 0 -9-0 2 Sin O + 3cos o -3=0 Sin O +los? = Sm?O =1- cos?O…

A: Form the given trigonometric equation in the quadratic equation than solve by factorisation.

Q: 6. Solve the equation cos z: V2 for z. COS Z =

A:

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

A:

Q: Find the exact value of the expression. sin 15° Z(/3+ 1) 4. 2W3+1) 4. EW3-1) 4. ZW3-1) 4.

A:

Q: 10 (217 2rx -i cos 11 2r7 Evaluate: (3n +2){E 11

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.