Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x 1+cos x 土, 2 b. cos - 1-cos x c. sin =±, 2

Q: 8. 9. A) 1−sinx Ĵ (COSX + 1 COS X+X 2(cosx+x)2 E) ·x)³ dx = ? 1+tan²a (2 + tana)² -+C B) +C D)…

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Q: 9 Find 0 if 0 < 0 < 2n and: e cos 0 = - f sin? 0 = 1 9 cos? 0 : 1 %3D /2

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Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

Q: 2. Express each expression in a simpler form. a) cos 0 sec e b) tan 0 cos 0 c) tan 0 + cot 0 d) VI –…

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Q: Slove and restrict solutions to exact values in the intereval [0, 2 ?)   A.    2sinx-cos^2 x=2…

A: Given : The interval [0,2),   A.…

Q: 1. What is the exact value of sin 75°? O -V6-V2 4 O vô-v2 4 O v2-V6 4 O V2+v6 4

A: We have to find the value

Q: 1. Use de Moivre's theorem to prove the trig identities: (a) sin 20 = 2 sin0 cose (b) cos 50 = cos'…

A: We have to prove this by demoviers theorem

Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

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Q: 2. If 5 sin 0 + 12 cos 0 = 13, then what is 5 cos 0 - 12 sin equal to? (a) -2 (b)-1 (c) 1 (d) 0

A: Here

Q: Prove algebraically that 1- tan? z sin(2r) ne 4 %3D 2 tan r cos? z - sin z The RHS (right-hand side)…

A: Please go through the attached solution.Thankyou . Best regards.

Q: True or False sin² 0 = 1 – cos² 0.

A: Use the trigonometric identity sin2θ+cos2θ=1 to verify the statement.

Q: 2) What is the cos Z? Express fractions in the lowest terms. NO DECIMALS 40 Y 9. 41 Your answer 3)…

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Q: 1- (tan z)? 1+(tan r)2 Use algebra to prove the equation cos s(2r)%3D

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Q: 7. The value of 2 cos (sin-1 (-0.6)) is: C. 0.8 D. -0.8 A. 1.6 B. -1.6

A: To find: The value of 2cossin-1-0.6. Formula used: cos-x=cos x Inverse trigonometry relation;…

Q: a sin if cos 0 = and 0 < 0 < b cos e if sin 0 = and < 0 < T C Cos 0 if sin 0 - 흥 and <0< 2T d sin 0…

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Q: 8. sin 2a = Zsn AcosA 24 25 12 25 9. cos 2a =

A: 8sin(2α)=2sin(α)cos(α)Let…

Q: Establish each identity.

A: 1+secθsecθ=sin2θ1-cosθ

Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: HW: (1) Prove that : cos e (a) sin e =1, (b) tan? 0.cos0+ cot? 0.sin?0=1 %D 1-tan 6 1- cot' 8 (h)…

A: Authoring guidelines:…

Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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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: – 1) sin a cos a - sin æ 9(cos² e – 1) O 9 tanx + 9 sec a O 9 cot a + 9 cscx O 9 tana + 9 csc a O 9…

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

A: To prove ..

Q: a) 2(sin x)? – 1 = 0 [0,27] b) 6(sin x)² + cos 2x + 1 = 0 [0,2n] c) (cos 2x)2 + cos 2x + 1 = 0 [- ,…

A: (a) ⇒2(sin(x))2-1=0⇒(2sin(x)-1)(2sin(x)+1)=0⇒sin(x)=12 OR sin(x)=-12⇒x=π4, 3π4 OR x=5π4, 7π4

Q: - and cos 0 > 0; f ind tan 0. 2 sin 0 = 2/3 (A 3 (3 B 3 -1 /3 D 3

A: As we know from the Pythagorean theorem, sin2θ+cos2θ=1 Given,  sinθ=-12

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos (a) Choose... sin (a)…

A: Trigonometric formulas

Q: Verify the identity: sin? 0 + 2 cos 0 – 1 1 sin? 0 + 3 cos 0 – 3 2 1- sec e

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Q: sin (x) = -0.9. If x and y are complementary, what is cos (y)? %3D Sub

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Q: 1 1 What is the equivalent expression of 1+cos(x) 1-cos(x) O a) 2 sec2 (x) b) 2 cos? (x) c) sec2 (x)…

A: 1)1/(1+cosx) + 1/(1-cosx).  2)sinx-cosx=0.

Q: I = cos? x sin x In(cos x)

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Q: 11. sin-(-0.99) 12. cos(-0.1)

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Q: 15. What is the exact value of cos (-15°)? O v6-V2 4 V2-V6 4

A: Cosine formula is given as, cosA-B=cosAcosB+sinAsinB Some values of trigonometry are,…

Q: 7. I. csc e - Cos 0 cot 0 = sin 0 II. (sin 0- cos 0)² = -1 COS %3D

A: Given that I. csc θ-cos θ cot θ=sin θ II. (sin θ-cos θ)2=-1

Q: (1) Evaluate xdx Hint: Express cos* x in terms of sin x. Then use the substitution u = sin x. Back…

A: topic - indefinite integral

Q: Verify the identity. 1 - cos e 4)- 1 + cos e COS sec 0-1 sec e +1

A: From the given problem:   1-cosθ1+cosθ=secθ-1secθ+1   L.H.S.=1-cosθ1+cosθ   As we know that:…

Q: 113. An Identity Involving Three Variables Suppose x = R cos 0 sin o, y = R sin 0 sin o, and z = R…

A: x=Rcosθsinϕ,  y=Rsinθsinϕ  &amp;  z=Rcosϕ. Now consider,…

Q: + i sin 12 22 = 2| cos 12 5m + i sin 12 5. Let z1 = 4 cos and 12 Find z,2, and

A: Given complex numbers are in polar form. For multiplication of polar numbers, the magnitudes are…

Q: 3-Expand In [x? sin' x /Vx2 +1] 4-if sin-10.6 = y find y and all six trigonometric functions from…

A: 4. We have sin-10.6=y⇒0.6=siny⇒610=siny⇒35=siny⇒sin(36.87)=siny⇒y=36.87we know that…

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

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Q: 12. The trigonometric identities applicable to evaluate [sin'0 cos³ e de 1. cos² 0 = (1+ cos20) I.…

A: Yhave have asked multiple questions and not mentioned which question answer you need so according to…

Q: 1+ sin 0 cot e Prove : 1- sin 0 (cos ece – 1}

A: Given:                            1+sin θ1-sin θ=cot2θcosec θ-12 Solve left hand side:…

Q: 3 10 28. tan cos Н. | 12 20 29. cos sin -1 I. T tan (sin- (-) J. - 4 K. -T

A: We are asked to match the following.

Q: Verify the identity. 5 cos(sin x) = V 25 25x2 %3D Let 0 = sin 1x → sin 0 = x = 4. -수 Thus, %3D %3D 5…

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Q: 3/3 find sin 0. 8. Given cos 0 = sin 0 = V[?] %3D

A: Given cos θ=338We know that sin2 θ+cos2 θ=1

Q: Solve for θ : (cos θ + i sin θ) (cos 2θ + i sin 2θ) …. (cos nθ + i sin nθ) = i

A: We have to solve for θ: (cos θ + i sin θ) (cos 2θ + i sin 2θ) …. (cos nθ + i sin nθ) = i Then we…

Q: a) Simplify cos "+ sin (3x) in terms of x . 2 [Hint: cos(A B)= cos Acos B sin A sin B1

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 3) tan? 0 – sec? 0 4) 1- cos? 0 1.092 5) (1- cos 0)(1+ cos 0) 6) (secx- 1)(sec x + 1) 1 1 sin? e 7)…

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Q: 2. If 5 sin 0 + 12 cos 0 = 13, then what is 5 cos 0 - 12 sin 0 equal to? (a) -2 (b)-1 (c) 1 (d) 0

A: We can find the answer as below.

Q: 1.2 Cos? x + 3 Cosx = -1,0<x< 2. 2 Cos2 0 = -3 Sin 0, 0 <e < 180° %3D TT

A: We have to find out As per guidelines we have to solve one question Please repost other question…

Q: 2 + cos 0 = 1 + 2 sin² 0

A: The given equation is  2+cosθ=1+2sin2θ The given set of possible answers is  -π3,-π4,π6,π4,2π3,π,3π2…