cos cos (x) y + sin sin (x) y 2cos (x) sin sin (x) – 1 y= = 3/2; 0 < x < %3D

Q: Evaluate the integrals

A: We have to evaluate the given integrals .

Q: sin x+cosX Differentiate y = %3D sin x-cos x 2 А. 1-sin 2x -2 В. 1+sin 2x -2 С. 1-sin 2x 2 D. 1+sin…

A: Given,  y=(sinx+cosx)/(sinx-cosx)

Q: cos x sin* x dx 2. [ cor'x sin'x de 1. 7/4 7/3 3. cos x sin x dx 4. /4 | cos³x sin³ x dx

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

A:

Q: COS X d) f(x)=3sin √√x³ -3x+2___ _e) ƒ(x)=! f) h(w) = 3 cos(tan w)

A:

Q: y" + y = 2 cos x – 2 sin x; y=x sin x + x cos x y" +y = sec x; y = x sin x + (cos x)In(cos .x)

A: We have two methods two check whether given function is solution of differential equation or not  i)…

Q: y- y' cos x = y² cos x (1 - sin x)

A:

Q: dy - x = x2 siny dx 3 -2 =-(-siny +cosy + Ce-y/?)*? ANSWER: x = + cosy + Ce

A: We will find out the required solution. Kindly note that there is misprints in question which has…

Q: 1 – sin(x) Evaluate: dx I+ sin(x) 1- sin(x) A cos(x) - 2x +C 2[sin (x) – 1] cos(x) -x+C 4cos(x) +C…

A: We have to solve the integration

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

A:

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: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

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

Q: cos(x) – sin(x) cos(2x) (c) lim (d) lim (cos())³/m²

A:

Q: Cos (x-y) t cos (Xty). COS 2cos x COSY

A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: (i) Express sinx – V3 cos x in the form A sin(x – a) with A > 0 and 0< a < - (ii) Find the general…

A: i) Given that expression is sinx-3cosx.It is required to write the given expression in the form…

Q: cOs x 1. S sin x (1 + cos x) ecosx dx

A:

Q: | cos xV 1 + cos x dx, -ㅠ <xSㅠ.

A: Given:   By part formula of integration: Here,  and and

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: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

A:

Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: cos 2x – cos x lim | x→0 sin x O -1/4 О 3/2 O -1/2 O -2/3

A:

Q: 1. S 2x sin-1 x² dx. 2. S sin² 20 cos³ 20 d0. 3. S sec? x dx V1-tan?x

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

Q: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

Q: sin x Check whether the function y = is a solution of xy' +y cos x with the initial condition y(r) =…

A:

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: sin- x - y· dx + (tan-(yx-1))xdy = 0 cos-12

A: The given differential equation is x-ysin-1yxcos -1yxdx+(tan-1(yx-1))xdy=0. Simplify to obtain the…

Q: (i) * cos x + cos x tan²x dx sec?x (ii) |x – 2| dx (iii) | x²/x* + 1dx

A: Since you have posted a question with multiple sub-parts, as per the company guidelines we will…

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: CsccSC X e coscoS X S- dx CoS x-1

A:

Q: (1-cos 6x)dx Perform the integration:S 1+cos 6x tanx - x +C c. tan3x – x+C A. -tanx – x+C D. tan3x –…

A: We have to choose correct option

Q: Function (y) 2 cos(x – 2n) Property -3 cos 6x 3 cos (x +) -2c05지 З cos Period Amplitude Min Value…

A: This question is related to trignometric ratios , We will solve it using given information.

Q: sin x Check whether the function y = is a solution of xy' +y = cos x with the initial condition y(T)…

A: Function is y=sinxx and the differential equation is xy'+y=cosx. Differentiating y=sinxx with…

Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

A:

Q: 5. (cos" x- y cos x) dr - (1 + sin x) dy =0

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: x²+1° w(x) = arctan x²-1, f. g(x) = ln (x³ – ) - g. f(0) = sin(sin(sin(0)))

A:

Q: 0sin 2 x coOS x dx

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: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

A:

Q: Explain why or why not Determine whether the following state-ments are true and give an explanation…

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

Q: cos 2x - cos2a Integrate cos x-cosa

A:

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

A:

Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

A:

Q: 3e" - 2 sec x tan x + cos x - 3 dx 1+x?

A: Given:

Q: 8. y'(sin x+ y) = x - y cos x

A: