Q3-Solving Trigonometric Equations 3n A) f(x) = sin B) Sin 20-cose-0

Q: 1. sin? 2x = 4 sin²x cos² x

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Q: Establish each identity.

A: Given sinθcosecθ-sin2θ=cos2θ

Q: 4 cot 0 sec 0 - sin 0 = O-4 4

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Q: Establish each identity.

A: The given identity is,  1-cos θsin θ+sin θ1-cos θ=2 csc θ The objective is to establish the…

Q: sin 0- cos 0+1 sin0+1 (c) sin 0+ cos 0-1 cos 0

A: Given: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

Q: Cos 40 x Cos 50 - Sin 40 x Sin 50.

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Q: Establish each identity.

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Q: 8. and tan 0 < 0 17 8. sin 0 csc e = cot 0 =

A: We are authorized to answer one question at time since you have not mentioned which question you are…

Q: 3. S sin* 2 x sin 4 xdx

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Q: sin 0- cos 0+1_ sin0+1 sin 0+cos0-1 (c) cos e

A: consider LHSLHS=sinθ-cosθ+1sinθ+cosθ-1multiply and divide by cosx LHS=(sinθ-cosθ+1)…

Q: SIne tand cose Cos cosA cos Sint sinf 1. sine 1 sine cose sine sin coso 1- cos-0 sin20

A: Trigonometry: It is a relation between the sides and the angles of a triangle. There are six…

Q: 1) sin 0 + cos 0 = sin 0 cos 0 %3D 1-cot 0 tan 0-1

A: To prove sinθ+cosθ=sinθ1-cotθ-costanθ-1

Q: 2. cot 0= sin 0 = cos 0 = tan 8 = csc = sec 0 = 2

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Q: Quadrants of: cos-0>0, sin -0>0   Quadrants of: cos 0>0, csc 0<0

A: We have to find quadrant

Q: 8. sin 0+ cos 0 = 1.

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Q: Method A: Method B: Replacing cosa by 1-sina. Replacing sin by 1- cos². Replacing seca by 1 + tan²…

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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: 8 b) tan 0 and sin 0 < 0 15 sin 0 cos 0 tan 0 sec 0 Csc 0 cot 0

A: Given that  tanθ = -815

Q: (sin-'(cos(2x) + cos-'(sin(2x).

A: Given : ddxsin-1cos2x+cos-1sin2x

Q: Establish each identity given in attachment.

A: Given equation: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

Q: sin S sin x cos* x dx

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Q: 3.Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter…

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Q: sine+sin20 18. Show that = tan 0 1+cose+cos28 Find the general solution of the equation sin4x- cos2x…

A: For Part (i) sin2θ=2sinθ·cosθcos2θ=cos2θ-sin2θ=cos2θ-(1-cos2θ)=2cos2θ-1 For Part (ii)…

Q: 1- cos () 1- cos(x) 1- sin°(;) 1+ cos(x)

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

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Q: sin 280 cos 160 - cos 280 sin 160. Express the following as a function of a single angle.

A: Here we have to exprees the function in a single angle.

Q: Establish each identity given in attachment.

A: To establish the identity, we need to prove that the left hand side is equal to the right hand side.…

Q: Establish each identity given in attachment.

A: Consider L.H.S. : sin θ+cos θsin θ-cos θ -sin θcos θ=sin θcos θ-sin θ cos θ -sin2 θ sin θ cos θ =sin…

Q: (3) Trigonometric Identities sin? 0 + cos² 0 = 1, sin? 0 = 1- cos² 0 cos? 0 = 1 - sin² 0 1 + tan? 0…

A: (a) Sin θ = 35     cos2 θ = 1- sin2 θ     cos2 θ = 1- 352cos2θ = 1625tan2θ = sinθcos θ2tan2θ = 352…

Q: cos2r - cos4r - Cos4r sin2r + sin4r cos2r + cos4r sin2r - sin4r = cot x tan x sin x COS X I3D

A: Solved the given problem using concept of trigonometric identities.

Q: sin(X)=3/5, X lies in 1st quadrant. Find cos(X)

A: The value of both sin x and cos x is positive in the first quadrant. Use the identity sin2x+cos2x=1…

Q: 1-csce Express in terms of cose and sine. cote A. cose – sine C.sine – cose 1-sine sine-1 D.2 cose…

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Q: single trigonometric 2. Simplify sin (3x) cos (4x) + sin (4x) cos (3.x). Express your answer as a…

A: To simplify sin3x cos4x+sin4x cos3x. To express the answer as a single trigonometric function.

Q: (sin 0+cos 0)² 3. sin?0-cos20 sin²0-cos²0 (sin 0-cos 0)²

A: (Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: ) cos(cos-¹(35)) ) sec(tan-¹(5)) csc(sin-¹(n)) ) cos ¹(cos(29°)) (4π) 5 =) sin ¹[sin ]]

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Q: cos 0 1-tan 0 1-cot0 sine 4. Show that = sin 0+cos 0

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Q: 3 [cot 0- sec 0- sin 0 O 1 -3 O 3 O 6

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Q: cos 0-2 cos 0 sin0 1-sin 0+sin²e-cos²0

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Q: S cos" 2 xdx Co.

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Q: 1+sine 3. - cose cose %3D 1-sine

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Q: cos 4x cos(-2x) – sin 4x sin(-2x)

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Q: sin0 - sece 8) cos0- csce 9) tan? 0 - cot? 0 1+ sine 1-sine 10) 1- sine 1+sin0 1 1 11) 1- sine 1+…

A: Question Number 8 Given expression sin θ - sec θcos θ - csc θ

Q: A water wheel rotates through the angle x, the water level L behind the wheel changes according to…

A: Definition used -                  Solution of a trigonometric equation -                  General…

Q: 2 sine – sin 20 lim 8--0 sine -0 cos0 Evaluate

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Q: 19.Solve the trigonometric equation:                        Tan x sin x  - tan x = 0    [ 0 , 2π)

A: The value of the tan function is 0 at θ=0, π in the interval [0, 2π). The value of the sine function…

Q: Solve using trigonometric Substitution: x'dx (4-x)

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Q: Sin 40 x Cos 20 + Sin 20 x Cos 40.

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Q: CoS cos 0 = 0 -

A: Half-Angle Identity:-

Q: sin²A = 1 - cos²A cos²A - 1 1 + cos²A

A: sin2A