(r + sin θ - cos θ) dr + r (sin θ + cos θ) dθ = 0

Q: X = acos'0 , y = b sin°0 %3D

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Q: Evaluate the integral given below

A: To evaluate the integral given below, ∫∫Rcosxsin2ydA, R=0,π2×0,π2

Q: sin r - cos z 2. 1+ sin(2r)

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Q: cos'r sin x + dy + (cos'x)y = 1

A: Divide by cos2xsinx on both sides of the given first order linear differential equation, then…

Q: cos ne sin no 4.0 |cosh t sinh t |- sin ne cos ne sinh t cosh t

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

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Q: bn= 는 Sin nT x dx ans=t- Excose LOS UTT sin

A: I have simplify and done step by step in detail...now hopefully you will get it.....go through the…

Q: sin30 de 10. J 1-cos e 11. J sin 20 sin 40 de. cos?30 d0 12. S 1 -cot 30 13. J tan 50 d0. 14. S csc2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: c. sin"(t)- cos (t) = 2sin (t)-1 = CS d. cot (2y)+cos?(2y)+ sin (2y) = csc²(2y)

A: Given,  c. sin4(t)-cos4(t)=2sin2(t)-1d. cot2(2y)+cos2(2y)+sin2(2y)=csc2(2y)

Q: sin(x – y) %3D tan x cot y - 1 %3D cos X sin y

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Q: cos(In2x) X A) cos(Inx) + c C) sin(In2x) + c dx = ? B) sin(Inx) + c D) E) 2.sin(In2x) + c 2…

A: Given indefinite integrals a) ∫cos ln 2xxdx b) ∫ex+1x+exdx Solve this integrals. Needed Formulae:…

Q: Verify the identity.

A: For the given identity, to prove the identity 1-cost1+cost=1-costsint…

Q: a Jx'cos(x')dr= a d. 1 sin(*) +C sin +C e -sin sin(x') +C sin(x 3 3 +C 3

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Q: sin 2t Cos 2t I) sec t = 1) sin t COs t

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Q: sin [cot(4e¬4*)]cos*[cot(4e¬4*)] dx e^x sin²(4e¬4x) Let u = cot(4e¬4x) %3D

A: Solution: Let the given integral is I=∫sin6cot4e-4xcos4cot4e-4xdxe4xsin24e-4x ......(1) Substitute…

Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

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

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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: cos(x + y) cos(x – y) = cos² x – sin² y

A: The objective of the question is proving trigonometric identities.

Q: x cos x Y = sin* cOS x find d dx | sin-

A: To  find: dydx=?

Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: sin (x) с. у c. y =: 1+cos (x)

A: Given :- y = sin(x)/(1+cos(x))  To find Second derivative of given function

Q: sin(x) + cos(y) 1 + sin(x) cos(y).

A: Given query is to find the dy/dx at x = 0 and y = π/2

Q: | cos xV 1 + cos x dx, -ㅠ <xSㅠ.

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

Q: (r + sin 0 – cos 0) dr + r(sin 0 + cos 0) d0 = 0 **

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Q: 30. y+y" = 0; 1, x, cos x, sin x, (-x, x)

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Q: sin(x+y)-sin(x – y) O cos x sin y = 2

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Q: cos o cos(x sin 0); p} = r(p) cos po CoS O %3D = cos ¢ sin (x sin o); p} = r(p) sin po %3D

A: We have to prove the following result Me-xcosϕcos(x sin ϕ);p = Γ(p) cos pϕMe-xcosϕsin(x sin ϕ);p =…

Q: SOLVE THE EQUATIONS

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Q: y = x + sin x, 0 ≤ x < 2π

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Q: cos r V1+ cos² x d dy sin

A: The integration with respect to 2 variables is carried out by integrating the inner differential…

Q: esin a x b. COs x dx 0.

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Q: dx i- xIn x cox + sin x dx. cos x- sin x i.

A: (i) The given integral is ∫1x ln x dx. Let u=ln x. Then du=1xdx. Apply the substitutions and…

Q: 1+ sin r , r < 0 f(x) = COs a sin x

A: Now, check the function is continuous at x=0 or not. Thus, the function is continuous at x=0.

Q: - sin x sin y y' cos x cosS y

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Q: 2 3. x = 1+ cos t, y = sin't

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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: 1. Evaluate: sin r dx COS x sin r cos r dr tan r dr COS dx tanx dr 1- sin r

A: Given: To find: The values of integral.

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

A: We have to prove given trigonometric equation is correct.

Q: (7-cos"(x) cos(x) sin(x) e dx = A) 7 ese(x) +esla(x) +C B) 7 sin(x) -x+etincx) + C C) other

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Q: X y' = A cos C 5 1 3 y =-X+-sinx + 2 sin(2x)- 32 1 -sin' x +5 24 5. 16 A = B = C =

A: We will use basic properties of sine and cosine trigonometric functions and basic knowledge of a…

Q: A. sin X = sin Y %3D B. cos X= cos Y C. tan X = tan Y D. sin X = cos Y %3D

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Q: I cos (x) sin(x) dx A. (sin²(x)) + C 2 B. (sin² (2x)) + C 2

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

A: Here is the solution of the given problem.

Q: sin x In y = x cos x – sin x+c

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

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