у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

Q: Find the expression , identical go Cat (9x) the given a. sin 46x) - sinx Cos x - sin(16x) b. cos…

A: Expression of cot(9x) : See all the options And use the trigonometric formula .

Q: (a) 1- + -...+(-1)"-1 (b) n/(n+1) (c) sin? k (d) sin k 1

A:

Q: 8. S sin x(2 – 3cos x)²dx

A: We have to evaluate the following integral.

Q: U= Sin/x-Y Show that +9u -tanu. 2.

A:

Q: y = 2 sin (20+ 4π 3 ^

A: Given query is to find phase shift.

Q: 1+cosx ction x= Correct yo 3

A:

Q: 2. tan x sec² x dx = when we set u(x) = and du = 00

A:

Q: =/2 4. cos z dr Jo da 5. I+1 I +IA

A: We have to evaluate the indefinite integral

Q: Let 3 sin z+ 6 cos y= 4.

A: The first derivative of y with respect to x is given by the expression . The second derivative of y…

Q: 14. y" – 4y' = -4te“, Yo = 0, yo = 1 26. y" +2y' + 10y = -6e¬' sin 3t, Yo = 0, yo = 1

A: 14. The given differential equation is, y''-4y'=-4te2twhere y0=0 , y0'=1 Take the Laplace Transform…

Q: 5. y=2 sin 20; 0=0,0=

A:

Q: ∫[(θ+3)sin(θ+3)dθ] Hint: Intergrate by parts

A:

Q: 7. S. 5x4x² 3 sin 2x y = 2 y = 4

A: Solution ) y = 25x .34x^2 Take log both side  log y = log ( 25x .34x^2 )  [ log m.n = log m + log n…

Q: Evaluate 7`-3z²+4x-8 dr dx 프(22+4) O In#(2? + 4)*| + In (2 + 4)* + -글tan 1 (플) + C Omp(22+4)| + -tan…

A: The solution is given below in the next step:

Q: using De Moiuve's theor@m, show Tsat sin50 = 16 sino -20 sin o + 5 sin o ニ Hense salve z4 K -30%+ Ex…

A:

Q: 4. When A + B + C = 180°, show that sin 2A + sin 2B + sin 2C = 4 sin Asin B sin C

A:

Q: 57 where 2 tan 0 = <0 < 3T 3 Find sin 20 7 24 24 25 24 25 25 24 4,

A: By using sin(2x) formula in terms of tan(x).

Q: 9 Determine fcot 20 sin' 20 d0.

A: 9. Given Integration can be simplified as

Q: 4.) y= Tan (x5) 5.) y= Sin x cos COS X tan x 6) y= 1- Sec x

A:

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

A:

Q: sech (Insinx) cotxdx=2tan-1(sinx) +C A True В False

A: Given integral is ∫sechln sinxcot x dx. The value of the integral is 2tan-1sin x+C.

Q: b. Z1= 4(cos 200° + i sin 200°), z2= 25(cos 150° + i sin 150°)

A:

Q: 2sinx if 2 sin x %3D what is u?

A:

Q: Evaluate V1-289z2 sin (16x) + C 17 1 sin 1 (17x) +C 17 sin (16x) + C 17 1. sin (17x) + C 17

A:

Q: Solve vxx + vyу %3D ху ,х € (0, п), у € (0, п ) v(0, y) = 0 v(п, у) %3 sin2y vх, 0) — sin3x v(x, 7)…

A: Given: vxx+vyy=xy   …1, x∈0,π, y∈0,πv0,y=0vπ,y=sin2yvx,0=sin3xvx,π=0 We have to solve equation (1).…

Q: 2πί -dz = 9. CoS z Iz=2 z3 + 9z :Select one True False

A:

Q: sin(2³ + 42) f(2) = %3D 2² – 2z + 5

A: In this question, we find the radius of convergence for the given function. For the radius of…

Q: 7) (r + sino – cos0)dr +r(sin0 + cos0)d0

A:

Q: = 4u ,u (0, y) =u (5, y)=u(x,0)= 0, u, (x,0)= 3, sin 27x - 2 sin 57x ,y >0, 0<x <5 70.3

A: Given                                            uyy=4uxx,   u(0,y)=u(5,y)=u(x,0)=0, uy(x,0)=3,…

Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

A:

Q: 1) y = 3sin(x) 2) y = 2sin(3x) 3) y = cos(-)

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: ngle Belo 1. Sin B = 30 34 2. Cos B = 3. Tan B %3D 16

A: Given problem:-

Q: Evaluate: Scos 2xdx cos2x, cos 2x +C A 2 6 sin2x sin32x +C 6. B 2 cos2x cos 2x + C 6. 2 sin2x,…

A:

Q: 7) sin Z 32 40 Y 24 9) cos Z

A: the objective is to find the trigonometric ratios.

Q: 5. 4 f sin + 2zdz

A:

Q: Evaluate: / sec (5x + 1).5dx Select one: O cor(5x+1) + c O tan(5x + 1) + c O cor(5x) + c O tan(5x) +…

A: Use the substitution method and simplify the given integration than integrate.

Q: 7. S sin*4xcos64xdx 3 I. 1. 512 3 I. 2046 II. 2048 IV.: 512

A: The given integral is ∫0π8sin44xcos64xdx To solve the integral we first simplify the expression and…

Q: T S. 12 sin² (u)du

A:

Q: sin'r dr

A:

Q: 7/4 26. * sec*e tan 0 de sec*0 tan*o de

A:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: Determine the value of R: 30 R² = (28.935)² + [R+R sec(- 1)]² – [2(28.935)(R +R sec(- 30 cos 56.565…

A: Given that, the function is R2=28.9352+R+Rsec302-12-228.935R+Rsec302-1cos56.565.

Q: 4+ 5x = sin (ry")

A:

Q: 9. y = 3 sin įx 11. y = 4 sin mx 10. y = 2 sin x 12. y = 3 sin 2mx

A:

Q: Гесos 4x sin 4xdx eCo:

A:

Q: 36) y = 2 sin x - 4 10+y 8-

A: to find the differentiation of given function.

Q: 6. ху\ + (1+х)y %3Dе*, у(1) — 0 7. sinx y'+2y cosx = sin2x, y : 2 6.

A:

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2