Prove the identity. sin x + sin 3x cos x + cos 3x tan 2x Use the Sum-to-Product Formulas and then simplify. sin x + sin 3x cos x + cos 3x 2 cos 2x cos x cos 2x

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

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Q: Verify the identity. (7 cos x-4 sin x)2 + (4 cosx+7 sin x)2 = 65

A: Given,           7cosx-4sinx2+4cosx+7sinx2=65

Q: Verify the identity. csc(x) cos²(x) + sin(x) = = = csc(x) cos²(x) + sin(x) = csc(x) 1 sin(x) 1 2…

A: Given csc(x)cos2(x)+sin(x)=csc(x)

Q: Verify the identity. 6 cos2(x) – 3 = 3 – 6 sin?(x) - (| ([ 6 cos?(x) – 3 = 6(1 3 - 3 = 6 – = 3 - 6…

A: Given: 6cos2x-3=3-6sin2x We have to verify the given identity. Formula used: sin2x+cos2x=1

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: Verify the identity: 1/(sin θ + cos θ)+1/(sin θ - cos θ) = 2 sin θ/(sin4 θ- cos4 θ)

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Q: 11. Prove each identity. cos 2x + 1 a) sin 2x = cot x h) CSc 2x + cot 2x = cot x sin 2x 2 tan x b) 1…

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Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: Expand and simplify: sin(x+3)-cos(+ x) 6 COS X

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Q: Rewrite – 6 sin(2) + 3 cos(x) as A sin(x + ¢)

A: Given data:   The given expression is -6sin(x)+3cos(x).   The given expression can be written as,…

Q: Lan: prove (:) - - 4. sin x tan =1- cos x

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Q: proof 1)  (sin x + cos x)2 = 1+ 2 . sinx . cosx 2)  cos4x - sin4x = cos2x - sinn2x

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Q: Prove an identity 6 tan x - 6 tan y = 6 sin (x-y)/cos x cos y Use a Reciprocal Identity, and then…

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Q: 1. Verify the identity. Show all steps. sin x tan² x-sin x = tan x (tan x – 1) cos x sin x+cos x

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

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

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Q: Verify the identity. (Simplify at each step.) cos³ x sin“ x = (sin“ x – sin x)cos x cos x sin“ x =…

A: Using First Identity Of Trigonometry.

Q: sin (1) Using an appropriate substitution, evaluate: [2+ cos(1) ]* 1 +C A 3[2+ cos(1)]³ 3 B +C [2+…

A: topic - Indefinite integration

Q: III. Verify the identity. 5.) 1-Cos 2x tan?x %3D 1+ cos 2x

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Q: Prove the identity. 1 2. = cos x tan x 2 csc 2x Choose the sequence of steps below that verifies the…

A: Given identity can be solve with basic trignometric relations.

Q: sin 20 Cos0 1+ Cos 20 = tan 1+ cos0

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Q: please help

A: To prove:

Q: Complete the sum identity. cos(0 + 9) cos e cos 0 – sin 0 sin 0

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Q: Prove the identity: 1 sin x COS X sin x + cos x (sin x + cos x)2 1+2 sin x cos x

A: Given- 1sinx+cosx-sinx(sinx+cosx)2=cosx1+2sinxcosx Here we will use the following formula-…

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: sin(cos-(0.7068)) O - 1.2926 O 0.7074 2.7074 -0.2926 1.7074

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Q: sin(cos (0.5354)) = O 0.8446 O 1.8446 O -0.1554 O -1.1554 O 2.8446

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Q: Establish the identity sin((3\pi )/(2)-0)=-cos 0. Which of the following four statements…

A: To find the correct option

Q: Jse the fundamental identities to fully simplify the expression. tan(x) sin(x) + sec(x) cos²(x)

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Q: Simplify: sin(-x) 1 – cos(-x 6 x 1 sin x cos x - O None of these -12 csc x -12 sec x 12 csc x

A: Sin(-x)        =-Sin(x) Cos(-x)        =Cos(x) Sin2x+Cos2x=1 cosec(x)       =1/sin(x)

Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

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

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Q: Establish the identity sec x - cos x= sin x tam x

A: GivenTo establish the identitysec x-cos x=sin x tan xFormula:sin2 θ+ cos2 θ=1sin θcos θ=tan θsec…

Q: Prove the identity. 4 sin(x - y) cos(x) cos(y) 4 tan(x) - 4 tan(y) Use a Reciprocal Identity, and…

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Q: Prove the identity. sin(x + y) – sin(x – y) = 2 cos(x) sin(y) Use the Sum and Difference Identities…

A: Given,

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: Verify the identity by converting the left side into sines and cosines. (Simplify at each step.) 7…

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Q: Prove the identity. 9 sin(x – y) cos(x) cos(y) 9 tan(x) – 9 tan(y) %3D Use a Reciprocal Identity,…

A: Given: 9tanx-9tany=9sinx-ycosxcosy As we know that the the trigonometric identities. 1).…

Q: Verify the identity. sin³(x) + cos³(x) = 1 – sin(x) cos(x) sin(x) + cos(x) sin3(x) + cos³(x) sin(x)…

A: we know that  a3+b3=a+ba2-ab+b2

Q: sin x+ tan x sin (2x) 5. Determine the non-permissible values of the identity 1+ cos x 2 cos x Cos3x…

A: Solve using properties trigonometric identities

Q: sin (x-b) If it is known that sin (b) = - 1, It is equivalent to 1+tan²(x)' O a) cos (x) Ob) – cos…

A: Some of the important identities of trigonometry are as follows:  sin2x+cos2x=1 secx=1cosx…

Q: Simplify sin “ z – cos“ æ O 2cos (x) - 1 O 2sin*(x) - 1 O 1+ 2sin*(x) O 1+ 2cos (x)

A: Using trigonometric identities.

Q: Prove the identity. Use the Addition and Subtraction Formulas, and simplify. cos(x) sin sin(x) -…

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Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: 1. Verify the identity. Show all steps. sin x tan? x-sin x = tan x (tan x – 1) cos x sin x+cos x

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

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Q: Prove the identity. sin x + sin 3x cos x + cos 3x = tan 2x Use the Sum-to-Product Formulas and then…

A: Given : sinx + sin 3xcosx + cos3x = tan2x

Q: Rewrite sin(x+5π4)sin(x+5π4) in terms of sin(x)sin(x) and cos(x)cos(x) using one of the following…

A: To rewrite sinx+5π4 in terms of sin(x) and cos(x) using sum/ difference identities.

Q: Verify the identity: (sin3 x - cos3 x)/sin x - cos x = 1 + sin x cos x

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Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

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Q: 2 – 2 cos 2.x 8. sec x csc x cot x + tanx - sin 2.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.