Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

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

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Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: Prove that cos(sinx) = /1 – x².

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Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: Prove that V1+ cos x +VI-cos x X +÷,0<x<. 4 TT - 1+ cos x -V1- cos x 2 2

A: PS: There seems to be a cut in the image. If this is the question, pls find below its solution.

Q: 1- , S" cos(x)esin(x)-8y dydx

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

Q: 5)Prove that (1+sinx)(1+sin(-x)) = cos²x (manipulate left side in order to get right side) %3D

A: We have to prove the given identity: 1+sin x1+sin -x=cos2 x We know that sin -x=-sin…

Q: tan(2x) O 1+ cos(4x) sin(4x) O cos(4x) – 1 sin(4x) O 1- cos(2x) sin(2a) sin(4x) 1+ cos(4x)

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Prove sin 2x cot x (1 - cos 2x)

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Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

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Q: * Prove: sin x = cos COS 2- 2cos x

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Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

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Q: Evaluate sin 2x sin 4.xdx 2 b. sin 3 2x + C 3 1 a. sin ' 2x+C 3 c. cos' 2x+C 1 с. 3 d. -cos 2x +С 2

A: To evaluate the given integral: ∫sin 2x sin 4x dx

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: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: Prove (Start either from the LI 1- sin x 2. cosx COSx 1+ sin x

A: To prove : 1-sinxcosx=cosx1+sinx

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y)= siny

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: 9. Prove. cos x sin x 1 - csc x %3D sec x

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Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

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Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

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

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Q: The proper transformation for sin²x to make the f sin²x dx readily integrable is {A} 1- cos²x {C}(1-…

A: Given the query is to find the correct option of integral.

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: prove that = - Cotx + C 1- cosx +Sin'x

A: According to the question, we need to evaluate the integration: F(x) = 2(1 - cos2x + sin2x) We need…

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Prove 2tan x cos (3x) = sec x (sin(4x) - sin (2x))

A: Topic- trigonometry

Q: 19. 2 sin 3x = V2 %3D 21. 2 cos (2x + 1) = 1 23. 2 sin (4x - 1) = 1 3x 25. 2 cos %3D EN =

A: The give trigonometric equation is: 2sin3x=2    ....(1) As we know that if the trigonometric…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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Q: x where 3π/2 ≤ x ≤ 2π. 1 + sec²x = 2 + cos²x + sin²x

A: Here we use formula of trigonometric equation.

Q: prove that catX+c - Cos'x+Sin2X

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Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

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Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: Prove (secx+tanx)/(secx-tanx) = (1+2sinx+sin^2x)/cos^2x

A: To prove that   (secx+tanx)/(secx-tanx) =(1+2sinx+sin2x)/cos2x

Q: cos(9x) -dx COS J 1+ sin²(9x)

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Q: What is the integrable form of sin-cos-sin0 do 2 2

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Q: Prove the identity. secx (1-sin'x) = cannot b cosx %3D

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Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

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Q: Show that n/2 sin x dx sin x + coS X %3D 4

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Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

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