x = 0 - sin 0, y = 1 – cos 0

Q: x=-2+4 cos 0 and y=1+5 sin 0

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Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

A:

Q: 플) - cos X = sin x 2.

A: cos(x-π2)=sin x

Q: (8 cos x + 9 sin x) dx

A: SOLUTION-

Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: · y = sin(cos 3x) – sin x cos 3x

A: Given : Y = sin(cos3x) - sinx.cos3x Let's differentiate:

Q: 1 - cos 4x 1 + cos x dx

A: The given integral,     ∫1-cos4x1+cosxdx

Q: 16. Calculate (sin 0 , 0 , cos 20) d0.

A: ∫0π< sinθ,θ,cos 2θ>dθ

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: Differentiate.

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Q: y = sin' x- cos 3 – cos' x cos³

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Q: 1.Solve tan y dx cot x dy = 0, cos y + 0, sin x

A: Here the given differential equations are 1st order linear differential equation. As stated we will…

Q: 2 + sin x Differentiate Y x + cos

A:

Q: 5. " cos (w) sin* (;w) dw -2n

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 15 cos(x) + 4 sec (x)dx

A: 1) I=∫15 cosx+4 sec2xdx =15∫cosx dx+4∫sec2x dx =15 sinx+4 tanx+c   (c- constant if integration)

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: sin (3x+1)dx 4 cos (3x+1) C

A:

Q: cos

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Q: what is y' of y=sin-1(cos x)

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Q: 2 - ƒ (t) = sin 0.5t + ²⁄t – 3 8 cos 32t

A:

Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: cos(3t) sin(8t) dt

A: we use  2 cos A sin B = Sin(A+B)-sin(A-B) sin(-x)= sinx

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: ∫cos(3t)sin(8t)dt

A:

Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

A:

Q: 37. 2(cos x)-/2 sin x dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: dr de sin - r- cos + eª cos = 0

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Q: 2x cos x? dx 1+ sin² x² 8

A:

Q: Differentiate.   y  = Cos h -1(Sin h x)

A: Given inverse hyperbolic function - y = cosh-1sinhxUsing Chain rule, differentiating on both sides…

Q: a) |(4 cos x+2cos x– 1)dx

A: we know the following identities   ∫cos(x)=sinx

Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

Q: dt 1. cos (2 sin 2r) V1-4r

A:

Q: cos (3x) · (8 sin (3x) – 1) dx = %3D

A: Given that : The integral is ∫ cos ( 3x ) ( 8 sin ( 3x ) - 1) dx  .

Q: a) v2 sin x = 1 =| 1 b) cos ( 2x 6.

A: (a) 2 sin x = 1sin x = 12sin x = sin π4General solution sinx = sinyx = nπ+(-1)n y general solution…

Q: 39. cos (T + x) 40. sin (2m- xr) 學一) 37T 42. cos 41. sin -

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

A:

Q: •π 2 (sin³r)√1 (sin³ x)√1 + cos x dx

A: Given problem:-

Q: 1. " x² cos 2x dx

A: (1) We need to evaluate the following integral ∫0πx2cos2xdx

Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

A:

Q: 1. y" + 4y = 4 cos x + 3 sin x – 8 %3D -

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: * /2 2 sinh (sin 0) cos 0 d0

A:

Q: 1.5; cOs X dx sin³ x – 4 sin x

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment