ifferential Equations: ind the general solution: sin x sec? x cos? y dx + dy = 0 . secx+ tan y = c . 2 tan x + sin² y = c

Q: (cos x cos y cotx) dx - sin x sin y dy = 0. -

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Q: Substitution Suggested by the Equation du/dv=sin(u+v) show complete solutions please

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Q: Solve the problem. sin x dx,n = 8

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Q: P sin(a)dz 1) Evaluate Væ² – 25 -da - ,. 2) Evaluate

A: Given, Part a: ∫x2sinxdx Using the By parts rule of the integration, ∫udv=uv-∫vdu Here u=x2 and…

Q: Evaluate COS (2x)sin(2a)dx

A: We have to evaluate  ∫cos4(2x) sin(2x) dx.

Q: V2 sin(20) = – 2

A: Given that the equation is                                                     sin2θ=-22 we have to…

Q: angles

A: As per policy, only first question is answered.  Please refer to the image below

Q: cos x 4 - 2 cos x COS X 9. Find dx (Please explain your answer).

A: Solving by substitute method we have

Q: y = [x + (x + sin² 3x)°]

A: Given query is to find the derivative of the expression.

Q: S(csc x cot a + 8x7)dx csc x x8 + c - cs x x8 + c - - - csc x + x8 + c - csc x + x8 + c O cot a + 8…

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Q: sin x (cos x + 4) dx 1+cos?x

A: Solution:

Q: (sin 20+1)d0 4. S sin²0+0

A: Given: I=∫(sin2θ+1)dθsin2θ+θ

Q: 2ª + e2" sin(2ª) dx sin(2ª)

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Q: sina+sinatan² dx a sinx 2. ·S

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Q: cOs x dx sin² x+ 2 sin x+5

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Q: sin 4x dx 1+cos22x

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Q: -sin x 0 [cos x - If f (x) = | sin x - 0, show that f(a)f (b) = f (a + b). 1] cos X %3D 0. 0.

A: Given: Here, f(a)=cosa-sina0sinacosa0001, f(b)=cos b-sin b0 sin bcos b0 001. Now,…

Q: 10. ſ sinx tan(cosx) dx

A: In this question, we need to integrate using the substitution method.

Q: sec0-1 sin 2 2. 2 sec e

A: Now,           since,half angle formula                                Sin Q2=1-cos Q2

Q: S(cscr cot a +4x)dx sec a +x"+c 4. CSc a +x +c sec a+ x"+c O - sin a + a+c CSC a+x"+c

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Q: sin cot-1 (2/20 CSC 2π 3

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Q: tan-1x dx. 1 + x2 Use an appropriate substitution to solve

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Q: 1 S- dx 4 - 9x2 а. -sin-1 -X+ c b sin-). Ос C.

A: Let  (3/2)x = sint So, x = (2sint)/3 Differentiate on both side  dx = (2cost)/3 dt

Q: f sin(5 - 6x) sin (6x + 5) dx

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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: D m 0=313 3. Q. I- A Cose C. COSE = Sine e. I Sec 20 b. Sin ²0+ - =1 1 d. _ _I tono It. f. 1+_ =…

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Q: t /2 ccosx CT-X sin(x +y)dy dz dx Jr/6 Jo

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Q: theater finds that there is a correlation between the number of ice cream flavors offered at its…

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Q: Solve the following trigonomehic equations and tind all solutions. a. Sin ex) cos (x) + Cos (2x) Sin…

A: Since you have asked multiple questions in single request  so we  will be answering only first…