1- 4cos*x = cos3x + 3cosx 2- Sin(In(i-i)) = 1 3- ((1+i)(1– i))' = (1+ i)'(1 – i)'

Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: 1 cos(5x) +... 25 cos(x) + cos(3x) + Ans. + 2 sin(x)+ sin(3x) +sin(5x) +...

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

A: Use the principal log to find z.

Q: 1/1+cos x + 1/1-cos x=2csc^2 x

A: Please refer the attached image for complete solution.

Q: If e/2i -/2i = sin2 then z = - 2i In(sin2) – 4kn 2i In(sin2)+ 4kT - 2i In(sin2) + 4kTt

A: Given: e-z2i=sin2

Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: Find all solutions to cos(7x)−cos(x)=sin(4x)cos(7x)-cos(x)=sin(4x) on 0≤x<2π30≤x<2π3

A: We know, cos(a)-cos(b)= -2sin(a+b)/2*sin(a-b)/2....(i)

Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

Q: 1-cos 3x +C dx 1+ cos 3x 3sin 3x

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Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: 8. f(x) = 2sin² 3x a. 12cos(3x)sin(3x) b. -12cos(3x)sin(3x) c. 12sin(9x)cos(3x) 9. f(x) = 3 cos² a.…

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Q: 12) Solve: (tan x) tan x = 0 X = 0 (2cosx+1) = 0 2 cos x + 1 = 0 2cos x = -1 m<x = 0% cos x = - m <…

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

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: 2

A: Prove: cos²(x/2)=(sin²x)/(2-2cosx)

Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

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Q: Solve exactly over the interval 0 ≤  θ  ≤ 2π 1. √3 Cosθ- 2sinθ cosθ = 0 2. Cos(θ/2) - cosθ = 0…

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Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: sin( 2 cos (x/ 20 )) = Select one: O 2x (400 - x )°/(400 - 2x) O 40 x/ (400 + x) O ( 2x - 400 ) /…

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Q: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: 1 sinx # 1-cos2x ẩu! (6 2

A: Given query is to find the value of the limit.

Q: 20. е -3.1х cos 2.1x, e -3.1х sin 2.1x

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Q: Evaluate cos x + 2 cos³ x + 1 dx cos' x cos4 x 7 +x + c 2 sin7 x sint x +x + c cos x +x + c 3. cos X…

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Q: 5. Find all solutions of 2 cos x- -cos x-1 0 if 0sxs2n.

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: integral cos^7(4x)

A: To find the integral

Q: Theory and Examples

A: limx→02x23-3cos x

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: 2. -1- -729630 -540 --450 –-360 270 -130 -90 90 130 270 360 450 5 40 6 -1- --2 -3- -5- y = 3 sin(x +…

A: The mid-line is the point of reference. So to find the mid line we have to find the average between…

Q: ( 2 3 2 cos* 3 sin dx O (3/14) cos*7 (2x/3) - (3/10) cos^5 (2x/3) + C O (3/14) sin^7 (2x/3) - (3/10)…

A: Here, we need to find the integral ∫sin323xcos423xdx. So,                ∫sin323xcos423xdxLet…

Q: 4. 1-3 cos x-4 cos² x 2 sin² x 1-4 cos x 1- cos x

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Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: 3.1 Find and classify singularities of sin) 3 -

A: Please check step 2 for the solution.

Q: (sin 4z + cos 4) O 2+ sin 4I COs 4r O 1+2 sin 4x cos 4x O 4+ sin 4I COs 4x O 1+2 tan 4x cos 4x O 1-…

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Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

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Q: 1 3n sin 3x + 3. |-23 8.

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Q: 1) / sen(x) 4+ cos²(x) I 1+4x² 2) [√5/2 S² 3) 0 4) 1 x² - 2x + 2 dx √ √2/2 are 0 X dr √2/2 arccos(x)…

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Q: 1- cos 4x sec2 2x – 1 = 1+ cos 4x

A: Question is solved.

Q: (cos^4 x) - (sin^4 x) = cos2x   verify the identity

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Q: COS 5x +COS 4 1-2005 3X フ JSecx# CSCX, a-X メtb

A: "Since you have asked multiple question, we will solve the first question for you.If you want to any…

Q: sin 0 13. Prove that 1 - = Csc 0(1 + cos 0). Cos 0

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Q: Prove: sin² x + 2 cos²x − 1 = cos²x -

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Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

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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: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: etan 4s | (cos (cos 4s)2 ds

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Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: Prove cos 4x = 8 cos4 x - 8 cos2 x +1.

A: In trigonometric ratio,cos2θ=2cos2θ-1

Q: Find x where 0 ≤ x ≤ 2π. cos²x - cos x - 2 = 0

A: