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: 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: sin(t) %3D 2. %3D

A: Solution - Given - Sint = 32We know that -Sinπ3 = 32Hence,Sint = Sinπ3t = sin-1sinπ3…

Q: angles

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

Q: .3 Cos x + cos x dx Vsin a 3,

A: Given…

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: 10. ſ sinx tan(cosx) dx

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

Q: Examine the change of the function and draw its graph: 2x-1 y =

A: Given: The function in x is given,           y=2x-1x3ex-1x Objective is to find the change of…

Q: L G -S 2 (5² +a²)2 11 t sihat 2a

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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: a 2. Find the exact value of cas(a) sin(b) given that a satisfies the equation 12a = 177 and b…

A: 12 a = 17π2b = sin-112

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…