Prove the identity. sin 2x- sin 6x - tan 2x cos 2x+ cos 6x

Q: las to rewrite the identities. b. sin(8x)-cos(8x)

A: a) We have to use the formula

Q: 1 + sin 0 1 + sin 0 1 - sin 0 |cos 6|

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Q: Verify the identity. cos3 x sin2 x = (sin2 x − sin4 x)cos x

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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: Verify the identity. cos(4x) = 1 - 8 sin?(x) + 8 sin“(x) cos(4x) = 1 - 2 sin?(2x) = 1 - 2(2 sin(x)·…

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Q: Prove the identity sin^2 THETA + cos^2 theta =1

A: Given: prove the identity

Q: II. Find tan (A +B) and tan (A - B) if: 5. cos A = - and sin B =, both A and B in QII.

A: As per bartleby guidelines we only give first question answers.

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

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Q: 20. Which expression is equal to + tan x using identities? tan x cos a 1 sin a cos x 1 sin x sin x…

A: According to the tangent identity, tan x=sin xcos x. So, substitute tan x=sin xcos x in the…

Q: Prove sin?x tan²x – cos?x = sec²x - 2

A: To prove : sin2x tan2x - cos2x = sec2x - 2

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: 4. Simplify the identity: cos 2 x - 1 Cos x + 1 COS

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Q: Prove the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

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

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Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

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

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Q: Use the addition formula to derive the identities. (a) cos(x – ;) = sin x (b) sin(x – 5) COS x kIN…

A: Addition formula are as follows: sin(A + B) = sin A cos B + cos A sin B sin(A − B) = sin A cos B −…

Q: Complete the identity. sin 2x- tan x = ? O A. tan x cos X O B. - tanx cos 2x O C. tan x cos 2x O D.…

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Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: VII. Verify the identity. 11.) sin 3x = 3 sin x-4 sin3 x

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Q: 1 cos 0 Prove the identity = tan 0. coc A 1tcin A

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

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

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Q: sin 2x 5. cot x = 1- cos 2.x

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Q: 1) Prove that cose-sin*e 1- tan?e cose

A: Trigonometric identities help to prove the required expression. The algebraic formula…

Q: Prove identity: 4 sin x cos x (1 – 2 sin? x) = sin(4x)

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Q: verify the identity

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Q: Prove identity (1+ a) (1 – cos a) = tan? cos æ) sec x x cos x

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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 cos2 θ/2 = (sin θ + tan θ) /2tan θ

A: sinθ+tanθ2tanθ=sinθ+sinθcosθ2·sinθcosθ=sinθcosθ+sinθ2sinθ=sinθcosθ+12sinθ=cosθ+12=2cos2θ22…

Q: Prove the identity. cos (x-y) sinx- sin(x-y) cosx= siny CoS Note that each Statement must be based…

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Q: 7. Prove the identity. 1-cos 20 tan 0 %3D sin 20

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Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

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Q: Rewrite -6 sin(æ) - 3 cos(x) as A sin(x + 4)

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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: Prove the identity Sin3A=3SinA-4Sin3A

A: Given identity is,Sin3A=3SinA-4Sin3A

Q: Verify the identity. sin 40 = 4 cos '0 sin 0 – 4 sin °0 cos 0

A: To prove that  sin4θ=4 cos3θ sinθ-4sin3θ cosθ

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

A: given trigonometric identity  Sin2x.cosx/cos2xsinx  Can be solved by using formula as shown below

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

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Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

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Q: Verify the identity. 2 tan(x) 1 + tan?(x) sin(2x)

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Q: Verify the identity. (1 – cos"(x)(1 + cot*«») = (1 - cos (x)(1 + cot°») - sin°C«) - 1 + sin (x) =…

A: Solved below

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

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