cos 2r + cos 2y cot (y - x) cot (y + x) (y + x) Cos 2r cos 2y 1

Q: 32. y" + y = sec x; y = c1 cos x + c2 sin x + x sin x + (cos x) In(cos x), (-7/2, T/2)

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Q: 2. 3- va(c + ian ) - va(0+ in ) Z1 = + i sin + i sin COs 22 = cos

A: This is the problem of complex analysis.

Q: А. у%3D —3 sin (2х — 3) + 1 (2x G. у %3D2 csc(x — п) Н. у %3D csc х + 3 В. у %3D2 sin (x +-) — 4 C.…

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

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Q: 2 3) Find the general solution to y' = sec x. 4) Find the particular solution to y' = sec x tan x…

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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)

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Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

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Q: cos 4z - cos 2z =

A: cosx−cosy​=−2sinx+y2sinx−y​2​

Q: 1/x COS 2º COS If f(x) = dz then 22 %3D 3 f'(x) = %3D

A: The given function is: f(x)=∫31xcos z9z9dz...(1)

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: 4 sin(x) cos(z) + 2 sin(z) – 2cos(z) – 1 = 0

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

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Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

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Q: y = 7 cos(x), y = 7 - 7 cos(x), 0 ≤ x ≤ π

A: The given equations are: y=7cosx, y=7-7cosx, 0≤x≤π To find the area of the region between the curves…

Q: | cos xV 1 + cos x dx, -ㅠ <xSㅠ.

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

Q: 0 2 1 X' =1 1 -2 X 2 2-1 -cos(1)[C(i+3) +5C,2C, + (3 – 1)C,] + sin()[G(i-1)-5G42G1-1(3-1)0 X(t) =

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

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Q: 0 0 1 cos(0) -sin(@)) sin(0) cos(0) 1 1 (a) (c) 0 1 0 (d) -1 | 1 0 0

A:

Q: Differentiate

A: Given: the function

Q: 5. y + 4y = sin x + 3 cos x Ans: y = C₁ + C₂ cos 2x + C3 sin 2x + sinx-cosx

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Q: cos cos 30 - cos 50 lim- 0>0 s 70 - cos 90 cos

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Q: Cos dx 32 osSsin) +2+c (주)-5cos주)+ 기+ C 35 32 -cos 35 32 cos 7 (2)- 32 cos(수)+C +C 4 Cos COS

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Q: cos 3z 3 cos 2z cos z = 2

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Q: 40. y = -3 cos x 39. y =-4 cos x 42 y= 41. y

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Q: cos 4B – cos 2B | 2 cos 3B sin В O -2 sin 3B cos B O -2 cos 3B cos B O -2 sin 3B sin B

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Q: 4. y= cos“ x, 0,27| Note: y'=-2sin x cos x, y"=2 sin? x-2 cos x

A: if the limit of the function (one-sided) at this point is infinite then the line x=a is a vertical…

Q: 9. y= sin (r - (z+ 10. y = sin 4 11. y = cos (x – 4. (z + 12. y = coS 13. y = 1+ sin x 14. y = -1+…

A: Matching the graph of functions given by questions 10, 12 and 14

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

A: The given identity

Q: (d) r(π/6 + At) - r(π/6) = √3 2 cos At sin Ar-1+(cos Ar i+ At + 2 3√3 2 -sin At 1 3/-)1 2 X

A: We can solve as follows

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

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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: Confused on this.

A: topic - trigonometric identities

Q: cos (2x direct method Solue cos(2X + 3y) by こ

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Q: cos(x)y' + sin(x)y = 2cos (x) sin(x) – 1 G) = 3/2, 0 <x < 2 %3D 2)

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Q: 12. y = 3 cos (2x) 14. y = -2sin(x) -1

A: We draw the graph of parent function.

Q: 1. 10 – (sec x + 1)(sec x- 2) 18 sin x cos x+ 12 sin x cos x-15 sin x cos x 2. 3 sin x cos x

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

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Q: √x(y)²-(√x cos √x - sec √x)y'=1

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Q: Test for exactness then solve. (cos x cos y − cot x)dx − (sin x sin y )dy = 0

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Q: (1 + cos x)y’ = sin x(sin x + sin x cos x – y)

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Q: cos (x+ y) cos (x-y) cos2 x- sin2 y

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Q: 2csc 0--cos Ocsc 0 + cos 0+2csc 0 a 5x Sa 7a A) 4 3 4 3n B) 0, 4 7x 4 T 37 C) 2 2 3 5x D) 2 3

A: cosθ=0 implies θ= (2n-1)π/2 , n is any integer. cscθ= 1 implies, θ=(4n+1)π/2 , n is any integer.

Q: Solve y′ + cos(x)y = cos(x).

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Q: 9. y"+y= sec² x Ans. y= c, sin x + c2 cos x0 + (sin x ) In(sec x+ tan x)–1

A: Let's find.

Q: sin 2 2) = (9z + 4), h(3) (2) (1) = sin(cos r), f"(1) %3D

A: