(ax) +k sin (ax) dx ka +sin (ax) а cos Evaluate e

Q: 2 sin A 1- cos A + sin A is equal to - then 1+ cos A+ sin A If y = 1+ sin A 1 y y O Option 1 O…

A:

Q: If e 2i =sin2 then z = = sin2 = 2 - 2 In(sin2) + 4kT 2i In(sin2) + 4k TI - 2i In(sin2) – 4k T | - 2i…

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

Q: 2 -3 sin x 2. Find + 4e*+3 dx. cos? x

A:

Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

A:

Q: If e /2i -sin2 then z = - 2 In(sin2) + 4KTO - 2i In(sin2) – 4kT 2i In(sin2) + 4k TO - 2i In(sin2) +…

A: Given e(-z/2i) = sin2 We need to find z. The solution is given below.

Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

A:

Q: cos*x If S(cos³x ·B) dx = + C, what is the B? 4 А. - sin x C. - COS X . 1 В. D. sec x CSCX

A: We have to find the value of B in the given question.  This question can be done by using…

Q: 1+cos 0 + sin 0 sin 0 Prove = 2 csc e 1+cos e

A: To prove : sinθ1+cosθ+1+cosθsinθ=2cscθ

Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

A:

Q: COS M + Sin n 2 secn COS n

A: we can solve by using trigonometric identities  Sin2x+cos2x=1

Q: 4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1) %3D

A:

Q: f1(x) = sin(x1) cos(x2), T f2(x, y) = xy, f3(x) = xx¹, € R² x = x, yern XER"

A: Given the following functions                  f1(x)=sin(x1)cos(x2),   x∈ℝ2f2(x, y)=xTy,   x, y∈ℝn…

Q: sin e 1 cos 0 Multiply - by 1 + cos 0 1 - cos 0

A: According to the difference of squares formula, (a+b)(a-b)=a2-b2. Using the difference of squares…

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

Q: sin(1) dt Using an appropriate substitution, evaluate: [2+ cos(t)]* A +C 3[2+ cos(t)]3 3 B +C [2+…

A:

Q: Find the limit.

A: Use the formula cosθ+ϕ=cosθ cosϕ-sinθsinϕ to simplify the term cosπ+∆x. Here θ=π and ϕ=∆x.…

Q: 1- co s x 1+co s x cos ae y = ln

A:

Q: 2) cos (0 + n) = -cos e =-COS

A:

Q: eiz-e-iz 1. Show that Sin z 2i

A:

Q: a) _*? (1-x²)Z x+3 b) S- x2+2x+5 c) Find the value of sin(tan-1- sec-d) dx d) S x² Vx2+1 e) S Vx2+2x…

A:

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

A:

Q: Ave homerks anly -Sinx de Je esCaK-Cotax tany 6) X-1 Sook cos X-4 da Cos X f(onx-Sinede

A: As per company's guidelines, I can answer only one question. To know rest please repost the question…

Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: у" + 25у %3D 0, у(0) 3 6, у'(0) 3D —4 Y(x) = | 5 cos( 5x) – sin(5x) sin (5x) x

A: We have given differential equation y"+25y=0 with initial conditions y(0) =6, y'(0) =-4 We have to…

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

A:

Q: Estimate cos E- 0.1) + cos

A: Follow the procedure given below.

Q: *y=(sin(x)+cos(x))cos(x). dyldx -sin 2(x)+cos*2(x)+2cos(x) -sin 2(x)+cos 2(x)-sin(2x) O

A:

Q: cos ax dx = xe", a 2 0. (or) Evaluate x' +1 cos ax 2: Prove that x +1

A:

Q: sin 0 + In + 22+3 = -3 1- cos 20 In y? + 322 - 4 = + 2ln y + 22 =-3 1+ (cot 0)2

A: Given system is  sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: 1 COS 4 Now, differentiate f'(x) with respect to x. - 4 -x* sin(x4) f"(x) = -x°•si Submit Skip (you…

A:

Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

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

Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

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: π/2 0 sin³ cos Ode 0

A: This question is based on substitution method.

Q: 1+ sin 0 b) coso coso 1- sin 0

A:

Q: X+1 1-x Select one: a. sin-1(x)-V1-x² +c www. O b. sec-(x)-V1-x? + c C. tan (x)-V1-x2 + C d. cos x)…

A:

Q: P8: sin x cos x -dx J (2 sin x – 1)(sin x + 1)

A: ∫1au+bdu =1a lnau+b+C

Q: 4 sin x cos x + 2 sin x - 2 cos x - 1 = 0

A: first factorize the given equation and than split two product equation  detailed solution is given…

Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

A:

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: 5. * S sin(1 – x) (2 – cos(1 – x))* dx A C (2-sin(1-x)5 +C (2-sin(1-x)5 +C+ D. (2-cos(1-x)5 +C…

A: topic - indefinite integral

Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

A:

Q: 1. Using Half Angle Substitution cos x dx Find= S 2-cos x

A:

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

A:

Q: (sin x)(cos x + 1) = 0 if 0 < x < 2n. А. п/3, 2п/3 В. О, п

A: This question is taken from trigonometry in which we have to find the roots of the given…