2 2 (5 cos? r* sin 0 drdodo: Tame 0 01

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30° 2.

A: Given to prove : cos30∘+sin60∘1+cos60∘+sin30∘=32…

Q: Express in the form a + bi where a and b are real numbers.

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

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: 24 cos 4x – 32 sin 4x а. (с, + 4x) сos 4x + (c, + 3х) sin 4x b. c,e2x + C2e 3x + 3 sin x C. none of…

A: follow the next step

Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2) and sin y=1/4 and y is in the interval (…

Q: Find all solutions to 2 cos(0) = 1 on the interval 0 <0 < 27 %3D

A: Given : 2cosθ = 1

Q: Prove the following inequalities (ii) -10|< sin 0 < |0| and -|0| < 1– cos 0 < |0|

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Q: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

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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: [o,1] Find the sne exponsion of fla)=x+2 in in Sine Sinlntix), %3D 00 4-(-1)^ %3D •Sin (nTx) (c) Sin…

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Q: 11T - If 0 = then 6. sin(0) = %3D cos(0) = %3D

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Q: Q3-Prove that (cos303cos³ 0-3cos 0 sin? 0)

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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: Evaluate the following integral. 3 4 4 cos '3x xp. sin 3x 1 18 4 4 cos '3x dx = V1- sin 3x 18 (Type…

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Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: 1, Solve for o 0-2T (a) sine 2 W cos 28 = 8- %3D O Zsin e- =o - omis ce)

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Q: If 0 = then 3 %3D sin(8) = %3D cos(e) = %3D

A: We have  this can be also written as

Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

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Q: 1) z = 6| cos 3T +i sin 2 +i sin 6 W = 12] COS 6 Find 2.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: - 47T then 3 - If 0 : sin(0) = cos(0) = COS Give exact values. No decimals allowed!

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: Given that cos ß = V3 find the exact 2 value of cos 2B: Cos 23 3 Cos 23 %D 1 cos 2B 1 cos 2B %3D II

A: Trigonometry Question

Q: 3.16. Show that 10 (1 – i)49 (cos + i sin ) (8i – 8/3)6 - V2. -

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Q: 2 7 sin a da 1+ cos z

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Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

Q: 1 ,3 -r/a0 ? 0 ,² dr sin0d0 ø do = x 32na cos X = ? 0 Jo Jo

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Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

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Q: 1 then sin 20 is equal to 2 If 20 is in QIl and cos 30 cos 0 + sin 30 sin 0 V3 1 1

A: The given trigonometric problem is solved below in detail.

Q: 3. Express into standard form: = = 8[cos (-5) + + sin(-5)] Z i 3 3

A: Solution

Q: b. Given that z = el®, show that z" += 2 cos ne. Hence, show that cos 50 = 16 sint 0 – 112 sin² 0 +…

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Q: 5- Prove the following (Answer two only): secA. secB.cscA.cscB a- cos*e – sin*o =cos²0 – sin²e c- =…

A: Answer 2 only.

Q: 3. Express M =cos 3A+cos A and N = sin 3A+sin A as a product form. M = cot 2A. N Hence, show that

A: topic- trigonometry

Q: Find all values of z: z = 4(cos 90° + i sin 90°) for n=2

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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: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

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Q: 0.3- Prove that: n 2n 1 (cos =0 +i sin8) + 10 2cosne - 5 eine

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Q: 2 =, where 0 < A < , what is the value of cos 4? 2 18+6/5 6. 18+6/5 18–6/5 6. V18-6/5 6

A: Use,  Cos (A) = 2 cos^2(A/2) - 1

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

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Q: 2. Find all possible solutions to the equation 2 cos 0 + v2 = 0. 0 in radians and let k represent…

A: To Determine: find all possible solutions to the equation .Express θ in radians and let k represent…

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

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

Q: sec 0 + In + 27+3 = -3 2 In y? + 327 – 4 = 1+ cos 20 2/1+ (tan 0)² + 2ln /y + 22 = -3

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Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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Q: de 2- sin(e) ( cos(e) de 1+cos(0) de 2- 3sin(e) de 3sin(e) + 4cos(e) + 5 de sin(e) + 3cos(6) + 3

A: SOLUTION Given ∫dθ2 -sinθ∫cosθ dθ1+cosθ∫dθ2-3sinθ∫d θ3 sinθ+4 cosθ+5∫d θsinθ +3 cosθ+3 we need to…

Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the…