a Find the values of A and B in the identity A (2 sin x + cos x) + B (2 cos x sin x) = 7 sin x + 11 cos x. 7sinx + 11cos.x b Hence show that dx = 1 -(5л + 6In 2). 2sinx + cosx

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: 14. Evaluate s sin x dx cos?x C. sec x +x² + C D. sec x -x? + C A. sec x 2x2 + C B. sec x + 2x2 + C…

A: AS per company guidelines we  are supposed to  answer only one question at a time. For solution of…

Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

A:

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

Q: 7) y=Flx)=cos" (x) A.) xCcoskl) =4 Cos? (x) %ax (coscx) =4 cas? (x) (-sin(x). 4 Cos (x)Sin(x) %3D…

A: Explanation of the answer is as follows

Q: If j(x) = e(sin(x)+cos(x))² , then j'(x) = 2 cos(2x)el+sin(2«) COS

A: Given

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the…

A:

Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: Which of the following is true? cos(x) + cos(7x) A Scos(3x)cos(4x)dx = J 2 J sin(4x)cos(3x)dx = […

A:

Q: 9 If f(0) = cos 0 · cos 02 cos 03 ....... cos 0n %3D f'() + tan 0,}=- f (8)] Show, {tan 0, + tan 02…

A: Introduction :

Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

A: Consider finding the root of f(x) = e-x(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

Q: Evaluate S sin“ (x) dx 4 Select one: -cos (x) sin(æ) +(x – sin(2a)) + C None of these 글sin'(2)…

A: ∫sin4x dx = ∫(sin2x)2 dx We have cos 2x = 1-2sin2x2sin2x = 1-cos 2xsin2x=1-cos 2x2

Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

A:

Q: Use integration by parts to evaluate 2x cos (x) dx (A А -x?cos (x) +c B - 2x cos (x) + 2sin (x) +c…

A:

Q: Q2- Show that, 2 sin x |Jo(x cos 0) cos 0 d0

A: We have to prove sinxx=∫0π2J0(xcosθ)cosθdθ                     (1) Since we know…

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: Evaluate: /sin(Vx)dx 2/x sin(/x)+2cos(/x)+ C B2sin(x)-2/xcos(x)+C 2/xsin(x)-2cos(x)+C D None of the…

A:

Q: The "equation cos x "y sin x is A Iny In (cos x) + k B Iny = In (sin x) + * c. Iny=-In(sin x) + k…

A:

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: -cos x + sin x in the form r sin (x + a), where r> 0, is: e A. 2 sin x+ -sin |x+ 4 B 57 2 sin x+ 4 2…

A: We will find out the required expression.

Q: Hi, there are two questions a) and b) attached  Thanks so Much!!!!

A: (a)consider the given complex number:

Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

A: Given

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

A:

Q: If sin x = siny = a and cosx = cosy = b, then cos(x-y) is Select one: O a. z2 + a² O b. 2b + 2a O C.…

A: Given  sin x = sin y = acos x = cos y = b Use cos (x-y) formula cos(x-y)=cosx cos y + sinx sinysin…

Q: 21. a. e x = sec sin z sin z) (e sin b. Ve Cos 2sinz 1 U e sin z COS d. cos x √1-e2sinz

A:

Q: Find all solutions to the equation cosx cos(3x)- sinx sin(3x) = 0 on the interval [0,27]. %3D O A. x…

A:

Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

A:

Q: 1) Using the formula: cos(x +y) = cos x cos y - sin x sin y, prove in steps that: cos? x = %3D 1+cos…

A:

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

A:

Q: 8. Evaluate (a) /sin z cos" z dr (b) / (ln z)* dz. You may use /In z dz = z ln z - z+c.

A: Let's find.

Q: Evaluate: /sin(Vx)dx A 2/x sin(Vx) +2cos(/x)+ C B 2sin(Vx)+2/xcos(x)+ C None of the given Choices O…

A:

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

A:

Q: dx 3. Evaluate cos“ 5x sinx 3sin( 2x) sin’x 5x sinx 3sin(2x), sin' x +C 24 A. 16 2 5x sinx 3 sin(…

A:

Q: 6. Which of the following is FALSE? 7. f A. (4 cos x-3 sin x) dx = 4 sin x + 3 cos x + C B. f3e³x dx…

A:

Q: 2sin (2x) cos(2x) dx = cos (2x) + C sin (2x) + C 6. the above the above cos (2x) + C 6. sin (2x) + C…

A: We need to evaluate ∫2 sin5(2x) cos(2x) dx                           (1) Let sin(2x) = t On…

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

A:

Q: 2. Show that: (i) sin (ii) A" cos (a + bx) = [2 sin bx + n cos - sin b (iii) A cot (a + br) = sin (a…

A:

Q: 1. Given sinx 12 and cos y : 13 both x and y lie in sxs, determine a) cos(x+y) b) sin 2y

A: Given query is to find cos(x+y) and sin2y.

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

A:

Q: х If f(x) = cos(1? + 1) dt, then find f'(x). %3D Select one: O A. None of the others O B. sin(x + 1)…

A:

Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: 9. Integrate the following: a) S sin? x cosx dx b) "(1 – cos 2x)/2dx

A: (b) The given integration is: ∫0π1-cos2x32dx To find the value of integration.

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: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

Q: St² sin(2t*)dt A 1 (sin(2t*) – 2t*cos (2t*)) + C (sin(2t*) – 2t*cos (2t*)) + C 14 B D (sin(2t*) –…

A: