Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

A:

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

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Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

A:

Q: Prove that: 1-tan? 0 cos? 0 - sin? e %3D 1+tan? 0

A: A function is said to be a rational function if it is given as the ratio of some values.  The…

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Prove : (1 - cos E)(1 + cos €)(1 + cot²0) = 1 %3D

A:

Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

A:

Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: Find the Integrationof {(u) = tanu + Cos 24. %3D

A: Consider the function, fu=tanu2+cos2u

Q: 82. Show that cos at cos bt %3D In

A:

Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

Q: cos 2x +1 Prove that sin 2x

A:

Q: Prove the following identity: 1+ cos(2y) sin(2y) 1+ cos(2y) sin(2y) 1 tan(y)

A:

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

A:

Q: 10. Prove that (지12 sin 8 cos 1 (cos a cosec 0) de 1/2-a (1-cos a )

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Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

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Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: Q/prove that : (cos x) = -Sin X %3D

A:

Q: 21 Prove the identity.cos x (1 ²x) 2 2. - sin sec X,

A: Consider the given identity cos2x1-sec2x=-sin2x.

Q: Prove that there exists a value of x so that -1 COS T = cosx %3D ned to

A:

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

A: Now we use identity  Sin2x +cos2x =1 And formula (a+b)2= a2 +b2 + 2ab  (a-b)2 = a2 + b2 - 2ab

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

A:

Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

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Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

A:

Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: 10. Prove that 7/2 TC sin 0 cos (cos a cosec 0) de /2-a (1-cos a). COS

A:

Q: 4. Prove that equations are identities. l– cos4x a) tan 2x =, 1+ cos 4x

A: Given:

Q: Prove the identity. ex(1- sin'x) = So cosx | %3D

A: Prove the identity- Secx(1 - sin2x) = cosx. We know that : sin2x + cos2x = 1 Here i attached…

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: VERIFY THE IDENTITIES

A: To verify

Q: prove it 5. 2 sin (3x) = 1– cos(6x)

A:

Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

A:

Q: 3 Verify the identity: csc (0) 1-cos2 (0) cos (20) 2 sin(0) + 2tan(0) cos(0) = %3D sin (0)

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Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

A:

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

A:

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

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Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: Prove that; (a) cos4θ- sin4θ = cos 2θ  (b) Sin (π/4 + A) + Sin (π/4 - A) ≡ √2 cos A

A:

Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

A: