2 sin 4x cos x LHS - 4(sin x cos x) (sin 4x)(cos x) 2(sin x cos x)( Use the Double-Angle Identities as needed, and then simplify by dividing out the common factors. 2(sin 2x)(cos 2x)(cos x) 2(sin x cos x)( LHS cos 2x cos x sin 2x cos 2x

Q: The value of cos x is given. Find sin x and tan x if x lies in the specified interval. cos x 3n CoS…

A: Given:  cos x=-45, x∈π, 3π2 To Find:  To find sin x and tan x for the specified interval.

Q: Verify the identity. (Simplify at each step.) sin1/2 x cos x - sin5/2 x cos x = cos³ x/ sin x sin /2…

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Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

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Q: sin (3æ) cos (4æ)dx 1 -cos (72) + cos (-a) + C 1 1 1 -cos (7x) + 14 -금in (7z) + 글sin (- 14 2 O A 1 1…

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Q: Rewrite sin(x - 15pi/4) in terms of sin(x) and cos(x).

A: We have to find rewrite sin(x-15π/4) in terms of sin(x) and cos(x) We know that  sin(a-b) = sinacosb…

Q: Prove the identity. sin(x -) - -cos(x) Use the Subtraction Formula for Sine, and then simplify.…

A:

Q: 65. 3 sin x = cos x 67. cosx- sin²x = 1 69. 2 cosx- 3 sin x- 3 = 70. 2 sin?x - cos x - 1 = C

A: 67. cos2x - sin2x =1 1 - 2sin²x = 1 Cos2x =1 2x = cos-(1) 2x = 0, 2π , 4π ..... x = 0,π,2π  So…

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

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Q: Verify the identity. cos 3x + cos x = 4 cos3 x - 2 cos x Working with the left-hand side, use a…

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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: 4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1) %3D

A:

Q: sin x - cos x = 1/5, what is (sin x) (cos x) equivalent to?

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Q: cos(2æ) Select an identity for cos(x) O cos(x) · cot(x) – sin(æ) O csc(x) O cos(x) – sin(æ) · tan(x)…

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Q: True or false: To verify the identity sin x 1 + cos x we should begin by multiplying both sides by…

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Q: sin? 0 1- cose (7) cos“ 0+2 cos0+1 1+ cos0

A: To prove ..

Q: 3下 2 cos x 1-Sin x

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Q: 1- sin 3 Cos B 1+ sin 8 Cos 3

A: We have prove the identity 1-sinβcosβ=cosβ1+sinβ , using trigonometric properties or mathematical…

Q: 3. Verify the identity cos(-a) 1- sin(r) COS 1+ sin(-r) =2 sec x cos(r) Show all work and justify…

A: We have to verify the identity cos(-x)1-sin(x) + 1+sin(-x)cos(x) = 2 sec x

Q: 2/2 and <x< 3 Зл find tan 2x. 2' 4. If sin x

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Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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Q: cos 5x - cos 3x = -8 sin? x(2 cos3 x - cos x) Working with the left-hand side, use a Sum-to-Product…

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Q: sin 0 1 + cos 0 Establish the identity: 2 csc 0 1 + cos 0 sin 0

A: given sinθ1+cosθ+1+cosθsinθ=2cosecθ

Q: 39. cos (7 + x) 40. sin(27 - x) 41. sin 42. cos + x 2

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Q: 10. Simplify (cos x- sin x)? - (sin x-cos x)'.

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Q: Simplify. 1+ sin 2x+ cos 2x COS X O A. 2(sinx+ cos x) O B. 2 tan x O C. 2 cot x O D. 2(sin x- cos x)

A: We have to silmplify

Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: Verify the identity. sin x- sin y x-y x+y cot = tan sin x+ sin y 2 2 Start with the numerator of the…

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Q: Describe what is wrong with the simplification shown. cos x - cos x sin^2 x = cos x - cos x (1 +…

A: Just simplyfing the above question we have

Q: 1. If tan x = -3.5 then tan(-x) = %3D 2. If sin x = 0.8 then sin(-r) = 3. If cos 0.6 then cos( r) =…

A: We know that  sin(-x) = -sinx cos(-x) = cosx tan(-x) = -tanx cot(-x) = -cotx sec(-x) = secx…

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

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Q: Verify the identity. sin x/ 1-sin x − cos x/ 1-sin x= 1-cot x /csc x-1 Working with the left-hand…

A: Take LHS and divide by sinx in both parts

Q: Simplify (cos x- sin x)(cos x+ sin x). sin x cos x O 2 cos x-1 2 cos x+1

A: Given: cosx-sinxcosx+sinx

Q: Which expression is equal to sin^4⁡x−cos^4⁡x / sin^2⁡x−cos2^⁡x using identities?   −1   2   1…

A: Topic- trigonometry

Q: Find the exact value of the expression whenever it is defined.

A: Given:a sinsin-1513- cos-1-35b cossin-145+tan-134c tancos-112- sin-1 -12

Q: Prove the identity. cos(x - 1) - sin(x + 1) = = 0 Use the Addition and Subtraction Formulas, and…

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Q: Show that the following is true. 3n sin - x) = -coS X We begin on the left side of the equation by…

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Q: Prove the identity. sin + x) + sin - -) =- = cos X We begin on the left side of the equation by…

A: Given sinπ6+x+sinπ6-x=cosx

Q: The value of sin x is given. Find cos xand tan x if x lies in the specified interval. sin x= xe 0 8…

A: Explanation of the answer is as follows

Q: Add Fractions sin x 1+ cos x 6. 1+ cos x = 2 csc x sin x

A: As you mentioned question no. 6 solved

Q: cos x – 1.75 = -1 COS X sin(4x) = 2 – sin 4x 4 tan(2x) – 1 = 3

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Q: Find sin(x/2), cos(x/2), and tan(x/2) from the given information. sin(x)=4/5 , 0˚< x < 90˚

A: Given,         sinx=45 , 0°&lt;x&lt;90° .

Q: sin θ = -4/5  ,3pi/2   4< θ < 2π Find cos(2θ).

A:

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?   −2   1   2   −1

A: We have to find

Q: 2 cos 2 ( x ) − 7 cos ( x ) + 5 = 0

A: Topic - trigonometric Equations Put cos 2x = 2 cos2 X-1

Q: Verify the identity. (Simplify at each step.) sin3/2 x cos x - sin72 x cos x = cos3 xV sin3 x .…

A: Here we solve the trigonometry equation.

Q: Simplify. 1+ sin 2x + cos 2x cos X O 2 cot x O 2 tan x 2(sin x + co x) 2(sin x - cos x)

A: Given: 1+sin2x+cos2xcosx

Q: cos(x + =) – cos(x – ) = 1 6. cos ( x 6. 6.

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Q: Simplify the identity :   :      sin2 x cos x /Cos 2 x  sin x

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Q: sin? ( * ) = 3 1- sec 2 ( * ) 3 1+ cos 2 ( *) 3 1- cos 2 ( * ) 3 1+ sec 2 ( * ) 3

A: Given query is to find the correct option.