How did the negative sign appear? To prove cos (iz) = cos h (z) = cos since et+e¬* eix +e-ix cos h (x) and cos (x) = 2 2 LHS=cos (iz) e(12) +e-i(iz) -e-+e? 2 2 RHS=cos h (z) : e+e=? Since, LHS=RHS.

Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

A:

Q: s nip

A: Given: 12cos2x+C=14cos2x

Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: n the der natwe of Sin (x )= Sin Cx-cos (rE)) to CoS

A: Definition: Differentiation is the action of computing a derivative. The derivative of a function y…

Q: Watch the video on the integral of sin(ax)cos(bx) and the video on the p two cosines with different…

A:

Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ> 0

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

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: 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: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

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

A:

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: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

A:

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Evaluate: 8 sin xcos xcos 2.xdx -cos 2x- 1 cos 2x +C 10 8 cos 2x--cos 2x +C С. A. 14 1 -cos 2x 10 1…

A: Integration is generally used to calculate area under the curve. When function definition changes…

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

A:

Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

A:

Q: |(4e + 3z² – 3 sin z)dz =. O 4e² +z – 3 cos z + c O 4e² +z³ – 3 sin z +e O 4ez + 13 + 3 cos z + c O…

A: integration

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

A:

Q: • If y = cos x2 + x² then • y(5) = 0 TO FO • If y = cos x² + x² then • y(3) = 4x² cos x²2 + 0 FO

A: Explanation of the answer is as follows

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: The value of the integral . rcos ydydr is cos 8 cos 4 b. - cos 8+ cos 4 2 1 c. cos 8 – cos 4 + Cos 8…

A: SOLUTION-

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

A:

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

A:

Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

A:

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

A: we use the formula ddx(ax)=ax lna

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: S cos(3z)sin1º(3z) dz A 1 (sin(3z))10 + C 3 C 1 (cos (3z))10 + C 3 -- 1 D 1 (cos (3z))'1 + C 33…

A:

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

A:

Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

A:

Q: The suitable substitution to evaluate sin 4(x+2) dx is None OA [1-cos8(v+2)] В. [1+ C. 2 + cos8(r…

A:

Q: F.(3e-3 sin(2x')) is equal to 2 3. n 4+@² 3 cos 8 4 3. 7(1+o² 4 cos 4 4 1 3, 1 +4cos 4. 4 2 1+@ 4…

A: Use the following formulas to calculate the Fourier cosine transform. Fee-ax=2πaa2+ω2…

Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: • Cos C = BE AC Cos 30°: y %3D 6.Cos 30', l603_ - 303 a %3D r 5.3 y: 313 5.2 yo

A:

Q: Q2:- Find fo, fe , fo if f(p, 0,¤) = p² cos ¢ sin 0. cos O sin 0

A:

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: 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: F.(3e-7 cos(3x')) is equal to 3. T9+o 1 -7 cos 12 4 O b. 2 3, T9+o 3 cos 9, 12 4. 12 3. 2 COs Va 4+o…

A: Using the Fourier cosine transform table, the following formulas can be written.…

Q: Find the solution of the equation zxx + zyy =e-xcos(y) which tends to zero as x-> ∞ and has the…

A:

Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: de 2- sin(e) ( cos(e) de 1+cos(0) de 2- 3sin(e) de 3sin(e) + 4cos(e) + 5 de sin(e) + 3cos(6) + 3

A: SOLUTION Given ∫dθ2 -sinθ∫cosθ dθ1+cosθ∫dθ2-3sinθ∫d θ3 sinθ+4 cosθ+5∫d θsinθ +3 cosθ+3 we need to…

Q: 2. Prove the reduction formula: (5 pts) n-1 sin x cos n - n-2 | cos" xdx = cos" xdx

A:

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

A: