31. (cos 40 + i sin 48)²(cos 30 + i sin 30) = A cos 50 + i sin 50 B cos 110 +i sin 110 C_ cos 30 + i sin 30 D cos 190 + i sin 190

Q: 1+ cos 40 cos* 20 do = .4 do = (1+2 cos 40 + cos 40) d0 1+ cos 80 de 4 3 + 2 cos 40 + 1 cos 80 do 1+…

A: Fully solve the intregal with each step

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A:

Q: Derive formula (2) on page 601. cosucos v 5lcos (u – v) + cos (u + v)]

A: Given equation is cosucosv=12cosu-v+cosu+v. cosu-v=cosucosv+sinusinvcosu+v=cosucosv-sinusinv

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A: Given query is to find the double derivative of the expression.

Q: Need help with explanation

A: 6) Solve the following:

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: Let z1 = 4 (cos 7π/12+ i sin 7π/12) and z2 = 2 (cos 5π/12+ i sin 5π/12) Find z1z2. Find z1/z2

A: Recall:  z1z2=r1r2cos(A+B)+isin(A+B) z1z2=r1r2cos(A-B)+isin(A-B) We have, r1=4, r2=2, A=7π12,…

Q: () TT sin TT 31. sin 32. cos cos 33. sin sin 4 34. cos cos 35. сos -1 cos 36. sin sin 6. 6 (c() 37.…

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Q: "(등 -2) + ain (품 + 22) The simplified form of cos 22x) + sin O V3 cos 22x + sin 22x O v2 cos 22x + 2…

A:

Q: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Approximate all solutions to 8.cos(x)2 –6.cos(x)+1 in the interval [0°,360°) X= degrees Round your…

A: The given equation is quadratic in cosx.

Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find all solutions in the interval 0° ≤ θ < 360° where θ1 < θ2 < θ3 < θ4 < θ5 < θ6. sin (30− 45°) =…

A: We need to find all solutions in the interval 0°≤θ≤360° for the given trigonometric equation.…

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: tan (+) = [² Lt) ton" (+ tan (4+/cmc+)) In 2 4 2 6 • tan À I 12 1²0 (+) - — tan² (+) + & tan² (+) +…

A:

Q: 9) -135° Pos Neg Sin Cos -:-

A:

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

A:

Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: Establish the identity. 1+ cos (20) + cos (40) + cos (60) = 4 cos 0 cos (20) cos (30) ... Choose the…

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Q: An expression that can be obtained from 13 sin 20 cos 20 5 4 sin 20 cos 20 + cos 20 i. 4 sin 20 + 9…

A:

Q: 7π/12+

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Q: M= sen 50° · cos 10° - sen 25° cos 35° sen 12,5 °. cos 12,5°

A:

Q: Express the number 8√3-6i in the form R(cos(0) + i sin(0)) = Re, where R> 0 and - ≤ ≤T. NOTE: Round…

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Q: 1/6 2 +3 sin 0 cos 20 1/6 2 +3 sin 0 (T %3D COS Gos 20

A:

Q: 1) Solve 3tan(x)=√3 over the interval [0,2π)  2) Solve 2cos(x)=2 over the interval (−∞,∞) 3) Solve…

A: 1. 3tan(x) = 3 tan(x) =13 So, x = π6or x = 7π6   2. 2cos(x) = 2 cos(x) = 1 x = 2nπ, where n = 0, 1,…

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: 7. Suppose x is a number such that cos(x) = sin(x). Then: O a) cos(2x) = cos(x) O b) sin(2x) =…

A:

Q: if cos alpha + 2 cos beta + 3 cos gamma = 0 ; sin alpha + 2 Sin beta + 3 sin gamma = 0 then  cos 3…

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Q: tan 30 + 2S in Go +Cos 30 -tan 60 4.

A:

Q: (sin 4z + cos 4) O 2+ sin 4I COs 4r O 1+2 sin 4x cos 4x O 4+ sin 4I COs 4x O 1+2 tan 4x cos 4x O 1-…

A:

Q: v3 V3 sin 30 = , cos 30° = , tan 30° = COS %3D O sin 30° = , cos 30° = . , tan 30° = %3D %3D V3, cos…

A:

Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

A:

Q: 20) sin(票 23) sin(一回) 21) cos (TT+e) 22) sin(277-e) 29) cos(年+e) 5TT 26) sin() 2テ) ton() 25)…

A: By bartleby rules, only first three questions have been answered 20.  sin5π12=sinπ2-π12=cosπ12…

Q: 1. tan 4 2. sin Зл 3. sin 4 4л 4. cos 3

A: There are multiple question. As per company policy kindly ask other question separately . 1.

Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

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Q: Ísin^8 (3z) cos^5 (3z) dz * O 1/27 cos^9 (3z) - 2/33 cos^11 (3z) + 1/39 cos^13 (3z) + C O 1/27 sin^9…

A: Given integral I=∫ sin8(3z) cos5(3z)  dz

Q: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

A:

Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

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

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Q: Select all the true equations. O cos(15) = sin(15) O cos(75) = sin(15) %3D O cos(75) = cos(15) O…

A: Use trigonometric angle conversion

Q: Compute cos² x dæ. cos 2x +C 4 cos 2x +C 4 2 sin 2x +C 4 2 O cos cos x +C 3 +

A: Formulae:

Q: 13л +i sin 16 5л +i sin 8. 13л 5л Let Z1 = 10| cos and Z, = 2| cos 16 8

A:

Q: (cos 20+ jsin 20) (cos 60+ jsin 60)1" (cos 30+ jsin 30)°(cjs 1000)

A: the given expression is cos 2θ+jsin 2θ5cos 6θ+jsin 6θ10cos 3θ+jsin 3θ9cjs 10θ Using De Moivre's…

Q: Approximate all solutions to 8-cos(x)² – 6·cos(x)+1 in the interval [0°,360°) x = V degrees Round…

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Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b

Q: 5. [(6+3z)cos(1+4z)dz 6. [2y° cos (9y)dy

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Q: 24. (sin 0°)(tan 30°) + cos 0° 26. cos 60°(cos 0° - cos 180°) 25. (cos 180° + 2 tan 45°) 27. (sin…

A:

Q: 5) 2/3cos Osin 0- cos 0 = 2cos 0

A: Please see the answer below.