In Exercises 59-68, verify each identity. csc 0 - cot 6 2 csc e sec 0 - 1 59. sin 60. sin 2 sec 0 sin 0 + tan 0 sec e + 1 61. cos 62. cos 2 tan 0 2 sec e tan a 63. tan; sec a + 1 sin a + 1 - cos a sin a(1 + cos a) 64. 2 tan sin x 65. cot 2 1- cos x 1 + cos x 66. cot- = sin x 67. tan co= = 2 csc x cot= 68. tan -2 cot x %3D OIN SIN

Q: Prove the identity. cos(x - ) - sin(x + =) - o

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Q: ) Prove cot 2 = tan u using the addition/subtraction formulas.

A: Given : cotπ2-u= tanu

Q: Verify each identity 1. sec μ - cos μ = sin μ tan μ 2. 1+sin λ / cos λ + cos λ / 1+sin λ = 2 sec λ

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Q: Verify the identity: tan (θ + π/4) =  (cos θ + sin θ)/(cos θ - sin θ)

A: We use the formula for tan(A+B)

Q: Write the expression sec(0) tan(0) in terms of cos(0) and sin(0). 1 cos(0) O sin(0) cos (0) O sin(0)…

A: We have to write the given expression in terms of cos and sin.

Q: prove the identity cos^3x sin^3x =(sin^3x-sin^5x)cosx

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Q: Prove the identity. sin^2(θ)−tan(θ)cos^2(θ)−cot(θ)=tan^2(θ)

A: We have to prove the identity                                         sin2θ-tanθcos2θ-cotθ=tan2θ

Q: Prove the identity. 2 tan 0 sin 20 1+ tan0 To verify the identity, start with the

A: Please refer to the image below.

Q: In Exercises 47–62, use a sketch to find the exact value of each expression. 47. cos ( sin ) 49.…

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Q: Verify the identity. tan (20) + cot (20) = sec (20) csc (20) Which of the following four statements…

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Q: Use the fundamental identities to match equivalent expressions. cos(8) – sin(0) a. cos(8) + sin(0)…

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Q: Verify the identity. sec 0- cos 0= tan 0 sin 0

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Q: In Exercises 60-61, verify each identity. sin 2r + (sin 3x + sin x) 60. cos 2x + (cos 3x + cos x) =…

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Q: Verify the following identities (tan 8 + cot 8)^2= sec^2 8 + cos 8

A: To verify the identity

Q: In Exercises 43–48, find the exact value of each expression. Do not use a calculator. tan 3 1 43.…

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Q: Prove the identity. cos²x 1+ sinx 1- sinx (1– sinx)? Note that each Statement must be based on a…

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Q: In Exercises 31–46, find the exact value of each expression, if possible. Do not use a calculator.…

A: Solution:Given31. sin (sin-10.9)32. cos(cos-10.57)33.sin-1sinπ3Formula:sin(sin-1x)=xcos(cos-1x)=x

Q: 1+ cos x (csc x+ cot x)² %3D 1- cos x 2.

A: Given : 1 +cosx1-cosx = (cscx + cotx)2

Q: In Exercises 25–28, sin t and cos t are given. Use identities to find tan 1, csc t, sec t, and cot…

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: Prove the cofunction identity using the Addition and Subtraction Formulas. tan ucot(u) TT 2 (3) is…

A: The identity to be proved is,

Q: Date Verify each identity. 1) cos (270° - 0) = -sin e 2) sin (90° + 0) = cos 0 3) cos (90° - 0) =…

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Q: To verify the identity: tan²θ+1=sec²θ , determine the value of tan²θ−sec²θ (for θ = π/4)

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Q: In Exercises 19-30, use a calculator to find the value of each expression rounded to two decimal…

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

Q: For Exercises 37-40, verify that the equation is an identity. (See Example 4) 37. sin(-x) + cscx =…

A: To verify:sin(-x)+cscx=cotxcosx Solution: Considering, LHS sin(-x)+cscx On simplifying further we…

Q: For Exercises 51-56, verify the identity. 20 _ csc 0 - cot 0 sec 0 + 1 51. sin? 2 52. cos? 2 53.…

A: To prove -  sin2θ2 = cscθ - cotθ2cscθ

Q: In Exercises 23–34, verify each identity. 2 cot 0 1 + cote 2 tan 0 23. sin 20 24. sin 20 = 1 + tan e…

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Q: Find tan theta if sin theta = 3/4 and theta terminates in QI. tan theta=?

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Q: Establish the identity. 9) sin(20) + cos 0 sin 0 = 3 cos Osin 0

A: Explanation of the solution is given below...

Q: 3. a)Prove the identity tan20- sin20 = sin²0 tan²0

A: We have to find the following conditions

Q: sec² () = 1+ cos x 2.

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Q: 9. Verify the identity. (1–cos² x)(csc x) cot x 2 sin x(tan x) a)a

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Q: 4 sin“ x = 1 – 2 cos 2.x + cos² 2.x

A: 4sin4x=(2sin2x)2 Using cosine double angle formula which is cos 2x=1-2sin2x1-cos 2x=2sin2x…

Q: 3. Which expression is equal to O - cos²x sin² x O - sin²x O cos²x secx sin x cotx+tan x using…

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Q: Prove each identity is true. cos x sin x 19. sin x + cosX %3D 1-tan x 1- cotx

A: tan x = sin xcos x= 1cot xl

Q: Use the cofunction identities to select the correct answer which fills in the blank. cos(10x) = sin_…

A: We know that, sin(90°+x) = cos(x) sin(90°-x) = cos(x)

Q: 2.2 State the identity that validate sin x = 3 cos x- and hence show that 6+9/3 tan x = [10] 23

A: Follow the procedure given below.

Q: Establish the identity. 1-2 sin 20 cos 20-2 sin 40 = cos (20)

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Q: Use a sum or difference identity to find the exact value. tan 10° + tan 20° 1 tan 10° tan 20° O A.…

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

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Q: Establish the identity 2 2 cos - sin 0 2, 1 - tan 0 2 = cos 0.

A: To establish the identity

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

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

Q: Date Verify each identity. 1) cos (270° - e) = -sin e 2) sin (90° + 0) = cos e %3D = Cos 3) cos…

A: We have to identify the following conditions

Q: 35. cos x + = sin x %3D

A: Solving the problem by doing the verification.

Q: Verify the identity by converting the left side into sines and cosines. sec(x) – cos(x) = sin(x)…

A: The given identity is secx-cosx=sinxtanx   identity used: 1-cos2x=sin2x

Q: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

A: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

Q: Suppose that tanɑ=-- and 90°<a<180°. 3 Find the exact values of cos and tan 2 2 cos Undefined 2 ? a…

A: Using trigometric ratios

Q: Prove the identity  cotx (1-cos2x)=sin2x

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Q: In Exercises 39-46, solve each product identities in the interv 39. sin 2r + sin x = 0 41. cos 3x -…

A: Note:- As per your demand we solve question 41 for you Given :- cos(3x) -cos(x) =0  To find:-…

Q: tan 45, sec 60 5 sin 90 sin 60° 2 cos 0 cos135° Leave your answer in exact form (no decimals). 11.…

A: We will directly out the values of all of these then calculate.

Q: Verify the identity: tan θ = (1 - cos 2θ)/sin 2θ..

A: Given, tanθ=1-cos2θsin2θ