Simplify the absolute value in 2 )sin u) if u = cos- 1 x/2for some real number x.

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

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Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

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Q: Show that (tan- x) = cos2(tan-1x) and then use Figure 8 to prove that (tan- x) = (x² + 1)-1. V1+x? y…

A: Given:

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

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Q: Prove : (1 - cos E)(1 + cos €)(1 + cot²0) = 1 %3D

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Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: 1. Prove cos 8-sin 8 cos 8 + sin e = sec 28 tan 20.

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Q: Prove the following: 1+2sin cos sino + cose = sin 0+ cos 0

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Q: Prove that 1- cos 2x = tan x sin 2x. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find all 0 in the interval 0 <0 < 2T satisfying tan(0) = - 0. Give all answers as exact values…

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Q: secx tanx :1 cosx cotx

A: Solving the proof by establishing the identities.

Q: Prove that Cot A Sec2A Sin2 A = Tan A. %3D

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Q: Beginning with [sin(x)]^2+[cos(x)]^2=1, prove that 1+[cot(x)]^2=[csc(x)]^2

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Q: Find the length of the path over the given interval. (6(0 – sin(0)), 6(1 - cos(0)),

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Q: prove the identy. sec θ − cos θ = tan θ sin θ

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Q: Show that os (2 tan~ r) COs

A: We have to prove that cos(2tan-1x)=1-x21+x2.

Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

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Q: Show that (tan−1 x)'= cos2(tan−1 x) and then use Figure to prove that (tan−1 x)' = (x2 + 1) −1.

A: The objective is to show that:  tan-1x'=cos2tan-1x.   Use the formula: ddxf-1x=1f'f-1x. Here,…

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: 2. Prove using the angle sum identity of sine: sin 90° = 1.

A: 2- Given- sin90°=1 To prove- The above expression using sum identity of sin. Identity Used-…

Q: (45°) – tan (45°). Give the exact value of sec 2, 1 2/3-3

A: Use the trigonometric table to solve the given problem.

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

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Q: Prove the following identity 1+ cos(2x) 1 sin(2x) tan(x) 1+ cos(2x) sin(2æ)

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Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

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Q: cos(Inɔx),>o

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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: Prove 4 (cos 10° + sin' 20° = 3 (cos 10° + sin 20°

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Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: Express as a sum.(sin ax)(cos bx)

A: Given : (sin ax)(cos bx)

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

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Q: show equation has at least one solution on indicated intervalcosx - sinx = x on (0, pie/2)

A: To prove that the given equation admits at least one solution in the given interval

Q: 3. Rewrite sec (tan-u+ cosv) (a, algebraic expression. as an

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Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: Prove the Identity 1-tan^4(x)=cos(2x)sec^4(x)

A: 1-tan^4(x)=cos(2x)sec^4(x)

Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: 4. Which expression equals 0? sin 50° tan 50° cos 50° O tan 50° – cot 50° tan 50° + sin 50° cos 50°…

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Q: Select all the true equations. O cos(15) = sin(15) O cos(75) = sin(15) %3D O cos(75) = cos(15) O…

A: Use trigonometric angle conversion

Q: 5. Restricting to the domain (0, ∞), let 1 1 = cos(=) sin(=)+= and 1 1 g(x) = (cos(÷) sin(÷)+ g(=) =…

A: Sine is a periodic function it dpes not approaches  any value as x approaches  to infinity

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

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Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: If sin theta + 2  cos theta = 1  then prove that 2sin theta - cos theta = 2

A: To Determine: To prove 2sinθ-cosθ=2 Given: we have sinθ+2cosθ=1 Explanation: we have…

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

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Q: if a cos0 - bsin 0 =c Prove that a sin0 + bcos0 = ±Va² + b? - c

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Q: Prove CotA= sin2A/1-cos2A

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Q: Prove using trig identities sin 20° =1 V3 cos 20° – 2 sin 40°

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Q: What is the simplified form of cos 10z-cos 42 , sin 102+sin 4æ O -tan(7x) O -cot(7x) O tan(7x) O…

A: We will evaluate the given form to simplest form as shown below

Q: Prove that _ d tanx = Sec'x.

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.