COLUMNA COLUMN B Derivative Functions 1) - cos-1 x x2+x sin 2x cos? x a. 1-sin x cos? x 2) csc x + 3 sec x b. 3) x2 tan x 3 sec x tan x- csc X cot x C. - 4) - cot-1x 1 d. 2. sin x -1 5) cos X e. 2+2x2

Q: b. cos ( I1/2 -x) c. cos(x+ II/2) d. tan(x+ II/2) e. tan( II/2 -x) a. sin ( I1/2 -x) 16. sin x 15.…

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Q: sec z- tan zr sin a sec a

A: To verify the identity:- sec x - tan x . sin x = 1sec x

Q: Find the derivative of the trigonometric function. y =  3(1 − sin(x))/2cos(x)   y' =

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Q: Use Theorem 1 to derive the formula.

A: Given  ddxsinx=cosxddxcosx=-sinx The trigonometric identity used here is  cot x=cosxsinxcosecx=1sinx…

Q: sin x sec x 13. cos x sec x 14. tan x cot x sin r + tan ! 15. 1+ cot A 16. tan ! ese A

A: To simplify the given trignometric fuinctions.

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

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Q: cos (x sin )=√₁ (x)+2 J₂ (x) cos 26+2 J₁ (x) cos 44+... sin (x sin )=2 J₁ (x) sin +2 J, (x) sin 36 3…

A: Using generating function of Bessel functions

Q: Verify the identity:

A: The given identity is sin3x+cos3x=sinx+cosx1-sin2x2

Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 1. y = 3 sin x – 4 cos x 2. y = x³ tan x 3. f(x) = cos x 1+sinx 4. y = csc x cot x f(x) cin?

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Q: Separation of Variable 1. (cos' x-sin x+ sin' x dx+sin x sin y(1- sin x \dy = 0

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Q: (tanz+cotr)-(tan'r+cos'r)-(sin'z+cot'r) -dz S x Lnx Ln (Lnx) Ln (Ln (Ln(x))) Ln (Ln (Ln (Ln(x)))) Ln…

A: Given: The integral is ∫tanx+cot x2-tan2x+cos2x-sin2x+cot2xx lnx lnln x lnlnln x lnlnlnln x…

Q: (sin x - cos x )² + 2cos x sin x

A: To simplify trigonometric expression

Q: sin x cOs x 1 – sin x 2sin x 2 cos x 3 cos x -1

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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: sec 2a cos ydy - (1 sin y) da = 0 %3D

A: Given:     sec(2x) cos2y dy-x(1-siny)dx=0 Re-arranging sec(2x) cos2y dy-x(1-siny)dx=0sec(2x) cos2y…

Q: Solve the equation for x, if possible.

A: Expanding along second column, we get

Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x) - cos (2x) 2. y =…

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Q: sin 2x+cos2x+1 1- Prove cot x sin 2x-cos 2x+1 2- Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: Evaluate the following 1-prove sin 2x+cos 2x+1/sin 2x-cos 2x+1=cot x 2-sinh(u-v) = sinh u.cosh v-…

Q: 1+ Cos(x)- Cos (x) Sin(x) + Cot(x) Sin(x)

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Q: (cos(2x) – sin(2x)cos(2x)) cos(x) – sin(x) For -dx=-F(x) + C. What is F (x)? 3 A (csc(x) – sec(x))3…

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Q: INTEGRAL OF TRIGONOMETRIC FUNCTION ∫ sin^2 (7x)dx Choices: A.) 1/2 x - 1/14 sin⁡14x + C B.) 1/2 [x…

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Q: S(csc x cot x + 7x°)dx O sin x – x' + c O cos x + x7 +c .7 O cot x + x' + c tan x + x' +c - csc x +…

A: To integrate.

Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

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Q: 5. If u and v are two velocities in the same direction and V th V u anh-1 = tanh-1 с с с educe the…

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Q: sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du…

A: It is given that    ∫cosx-tanxcos2x dx We have to evaluate it.

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

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Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

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Q: B. Involving Trigonometric functions sin cos cos w sin w) dw üi) sec"(3y)tan (3y)dy iv) | tan…

A: Since, Since,

Q: sin () if x + 0, COS X Let f : R → R be the function given by f(x) if x = 0. -1

A: The function  f:ℝ→ℝ is defined as follows: fx=sin1xcosx  if  x≠0-1                    if  x=0…

Q: EQUATIONS REDUCIBLE TO EXACT EQUATIONS RULE 1   (sin y + ysinx)dx - (cos x - xcos y)dy = 0

A: sin y + ysinx)dx - (cos x - xcos y)dy = 0

Q: I+ cosx+ cos 2x (ii)Show that sin x+ sin 2x tan 20 - tan 0 = tan 0 sec20 cotx (iii) (iv) (cose -…

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Q: I. Matching Type Direction: Match Column A with Column B. 1. e* a. cos x +i sin x b.-+-+.+(-1)-1 b.-…

A: We need to match column A with column B:

Q: cos e - sin 0 Find a closet rank-1 approximation in the l² norm to A = %3D sin 0 cos 0

A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

Q: Find the limits in Exercises 25–30.

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Q: (1+ cot x) dx Evaluate: sin?x/9- cot?x cotx (А) - sin +C 3 9- cot?x – sin cotx + 9- В - cotx + C - -…

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Q: 6(cos² x – 1) sin a cos x – sin x O 6 sin æ + 6 cos e O 6 tan x + 6 sec x O 6 tanx +6 csc x O 6 cot…

A: We need to simplify the following expression 6cos2x-1sinxcosx-sinx

Q: S(csc a cot x + 6x³)dx %3D - sin x + x6 +c - sec x + x° + c csc x + x° + c 26 O sec x + x° + c 6.

A: To evaluate ∫cscxcotx+6x5dx

Q: sec4 x 21) tan3/2 x A) _ -1 + C tan1/2 x B) - 14 tan- 1/2 x sec4 x + 7 tan-3/2 x sec5 x+ C C)? tan-…

A: Here is the solution

Q: cos(-r) 1-sin(-z) 3 x 1+sin r COS T 6 csc z 6 csc z 6 sec 2 06 sec I 3.

A: Trigonometry problem...

Q: 3(cos? z – 1) sin x Cos x sin x O 3 cotx +3 sec x O 3 cot x+3 csc x O 3 sin x +3 cosx O 3 tan +3 sec…

A: The given question has been solved in detail with the help of following identities (x^2-y^2) =…

Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

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Q: sin x b. 1+cos x 1-cos x sin x

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Q: / [cos(x) – sin(x) ]dx Evaluate: A -cos(x) + sin(x)+C B ® cos(x) – sin(x) +C © - cos(x) – sin(x)+C D…

A: We know that integration of sinx is -cosx  And integration of cosx is sinx. Here i attached solution…

Q: INTEGRAL OF TRIGONOMETRIC FUNCTION ∫sec^8 (1/2 t) tan^4 ( 1/2 t) dt Choices: A.) (tan^8 (1/2 t^3…

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Q: 1- sin(x) A cos(x) +x+C COS 1+ sin(x) B -x+C cos (x): cos(x) -+C cos(x) – x 2cos(x) D 1+ sin(x)

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Q: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos…

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