cos(x) = 3/6       3?/2 < x < 2? cos(x/2)=? sin(x/2)=? tan(x/2)=?

Q: If e 2i =sin2 then z = = sin2 = 2 - 2 In(sin2) + 4kT 2i In(sin2) + 4k TI - 2i In(sin2) – 4k T | - 2i…

A: Given that, e-z2i=sin2e-z2i=sin 2e-z2i×ii=sin 2eiz2=sin 2

Q: 3. cos x +sin x- cos(2x) sin(2x), cos(3x), 4 8. ...

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Q: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

Q: cos x-2 cos 3x + cos 5x b. cos x +2 cos 3x + cos 5x :-tan x. %3D

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Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

A:

Q: cos 2x–1 lim COS х— 1 cos x-1

A: limx→0cos 2x-1cosx-1

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

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Q: 7. cos 2x- cos x -2 = 0

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Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: b) (cosx+ Sinx)² - Cos x+sinx)(cosx-Sinac) tan 2x 2. c) 1-Cos-x - Sin2oc) Sin X - 2cos x

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Q: sin- In2 4+ tan-'cos- dx 2 2 I+ cos2* 4+ tan-'cos- In2 4+ tan-'cos- dx 2 2sin- 2 A 1+ cos 4+ tan…

A: To evaluate: ∫sin x2 ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: sin- In?| 4+ tan-!cos- dx 1+ cos2- 4+ tan-cos- 2sin- In2 4+ tan-'cos- dx 2 2 A 1+ cos 4+ tan-'cos- х…

A: Given integral ∫sin x2.ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: Cos 3.x - cos 7x 53. sin 7x + sin 3.x cos tan 2r 54. sin = %3D

A: We can verify question no 53 as below

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

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Q: sin xV1+ cos 2xdx 6. V1 - sin 2xdx 7. 8. cos' xdx 1+x+x? -dx x² + x3 9. I sin 2x 10. I + sin² x xp-

A: Note: As per company policy we are supposed to solve only one question, So kindly repost the other…

Q: 20. cos x 3 cos x -V2 cos x csc x; xe[0,2n]

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Q: cos 2x - 2 sin x- cosʻx=-3

A: Consider cos 2x-2 sin x-cos2 x=-3  . . . . . (1) We have cos 2x=2 cos2 x-1 . . . .  . . (2)

Q: sin In 4+tan cos-dx 4+tan-Icos- 2 1+ cos 2sin In4 4+ tan cos- dx A 1+cos 4+ tan-cos- 2sin-In 4+…

A: To rewrite the given integral so that the integral can be evaluated easily. ∫sin…

Q: 1. S 2x sin-1 x² dx. 2. S sin² 20 cos³ 20 d0. 3. S sec? x dx V1-tan?x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4 cos (4x)(-4 sin (4x))dx. Evaluate the integral 4 cos (4x)(- 4 sin (4x))dx%3D

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Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

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Q: 6. h(x) = 5x sin-1x 7. h(x) = tan x – tan-i x 8. h(x) = 3 sec-x 9. h(x) = 14 cot"x+ 12 cos-x 10.…

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

Q: x = -30°, cos 2x = 1 - 2 sin2 x 1 + 2 sin 2 x 1 - 2 sin 2 x 1 - 2 sin x 1 + 2 sin x

A: This question is based on Proving a Trigonometric equation.

Q: x*sin (2x) dx a. ** cos(2x) – x³ sin(2x) –r² co. 3 x² cos(2x) +x sin(2x) +- cos(2x) + C 4 1 cos(2x)…

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Q: 1- cos 2x 2 1+ cos 2x 1 (1- cos? 2x)(1+cos 2x) dx = 8. 8.3.25 sin2 z cos a dx = 1+ 8 dx = cos 2x -…

A:

Q: Solve sin(x) = -0.32 on 0 ≤ x < 2π

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Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: cos" x dx Cosn-1 x sin x n – 1 + п-2 Cos' x dx n n

A:

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

A:

Q: 2 sin'x - cos x sin'x - (1 - sin'x) in*s) Rule ? %3D sin°x - 1 + sin´x Rule ? %3D = 2 sinx - 1 Rule…

A:

Q: Graph the functions in Exercises 13–20. What is the period of each function?

A: Dear student, Since you have posted multiple questions, as per our policy we will answer first…

Q: sin-- In?| 4+ tan-'cos- dx 2 1+ cos 4+ tan-'cos- In| 4+ tan-'cos- dx 2 2sin- 2 A | 4+ tan-!cos÷ 2 1+…

A:

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

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Q: 1. Lim 2×ー2xーメ+1 x-x3- 2x + 2 3. Lim メ→。 |- Cos X X-1 Sin 2x 2. Lim csc ax Csc 2x 4. Lim 7X 2x+5 x-…

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Q: cos 2x 25. cos x- sin x A sinx cos X cos x + sin x 2 cos x + sin x cos x - 2 sinx B 2 sin

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Q: Scos“ x- sin' xdx x•sin³ xdx 3

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Q: 4. 4sin(x)cos(x)+2 cos(x)-2 sin(x)-1=0 -13D0

A:

Q: (1) f(x) = sin (5x + 6) (3) f(x) = sin(x-³) (2) f(x) = sin (3x4 + 2) (4) f(x) = cos (4+ 3x)

A: To find f'(x)

Q: 5. у %3D sin? (3x2 — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) =…

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Q: cos x 13. lim x-(7/2)* 1 – sin x e21 – 1 15. lim - -0 sin t 1 - sin 0 17. lim 0/2 1 + cos 20

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Q: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: In2| 4+ tan-'cos- dx 2 sin ( 1+cos | 4+ tan-'cos- 2sin- · In²| 4+ tan-'cos- dx 2 (A 1+cos- 4+…

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Q: solve it 1- cos x 37. 1+ cos x 3 38. sin x = cos 2x 39. tan'x + tan?x – 3 tan x – 3 = 0 40. cos 2x…

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