If n e N, then (1 + i V3)" + (1-iV3)" is equal to: إختر أحد الخيارات NTI .a 2" cos 3 None of these b NT .c 2n+1 cos 3 NM .d 2" sin 2 2n+1 sin NT e 3

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: 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: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: Find the value of 2 32 tim (22 (1 - cos (2) - cos (4) + cos (2) cos (=))} x →0 8 X

A: Sol:- limx→032x81-cosx22-cosx24+cosx22cosx24Expand…

Q: 2 Given tan 0 = -and sin 0 > 0, find cos 0. %3D Cos 0 _ 3/13 13 О А. O B. cos O 0 = 3/13 COS %3D 13…

A: The given data is: tan θ= -23  and  sin θ&gt; 0

Q: (a) Show that z" + z=" = 2 cosn0. (b) Hence show that 32 cos5 0 = A cos 50 + B cos 30 + C cos 0…

A: Given:- Let z= cosθ+ i sinθ

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: 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)

A:

Q: Find the exact value of cos(2θ)cos(2θ) given cscθ=85cscθ=85 and 0<θ<π20<θ<π2 cos(2θ)=cos(2θ)=

A:

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

A: 8sin(2α)=2sin(α)cos(α)Let…

Q: Prove that .. ICOS 55 577 3 Cos БП [Cos 4 isin STT 3 57 + i sin S11114 = ~1 6 G +

A:

Q: snip

A: sin4θ=sin2θ2=1-cos2θ22=141+cos22θ-2cos2θ=141+1+cos4θ2-2cos2θ=14+1+cos4θ8-12cos2θ=14+18+18cos4θ-12cos…

Q: Find 0, if 0° <0 < 360° and 1 and 0 in III. 2 cos 0 =

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

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: 3)* dr sin 20 Find if r = do 1+cos 20 dr dr d0 1+sin 20 do 1+ cos20 OOption 3 O Option 4 de sin 20…

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Q: The entrance of Angel Stadium in Anaheim is cemposed of baseball bats configured in various right…

A: Given∠DCE =34°CD =47

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: 10. Prove that 7/2 sin 0 cos ! (cos a cosec 0) d0 /2- TC (1-cos a). COS

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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: Find the exaet values of sin 20 and cos 20 for cos 0= 3 on the interval 0° ses 90°. 18 V35 17 cos…

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Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: Find the solution(s) to 6+5 cos (-) = 10 that are in [0, 38]. Use at least 4 decimal pla- %3D

A: Answer

Q: Find the first step in the following "Proof" that is incorrect, and explain in a short paragraph why…

A: We are asked and said that the griven proof contains incorrect proof to which we need to find in…

Q: 125 cos – j sin 11 7T 11 1. Simplify . Express answer in rectangular form. 47 + jsin 11 J5 cos 11

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If cos 0 = 0.9, find the value of cos 0 + cos (0 + 2x) + cos (0 + 4x). cos 0 + cos (0 + 2n) + cos (0…

A: Given, cos θ=0.9

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

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Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: find exact value 197 8. (a) cos 6 (b) сos 6 (c) cos 6 9. (a) cos 4 (b) cos 4 (c) cos 4 10. (a) sin 4…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

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

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

A: Solution

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: If 20 is in QII and cos 36 cos 0+ sin 30 sin 0 = then sin 20 is equal to 2 O V2 O V3 2 0 1 o 1

A: cos 3θ cosθ+sin 3θ sinθ=-12

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

A:

Q: 1. By considering (1+ expi®)", prove that "C, cos r0 = 2" cos"(0/2) cos(n /2) (ii) ►"C, sin r® = 2"…

A: First, expand the given complex function:

Q: Q3-Prove that (cos30=cos³ 0-3cos 0 sin? 0)

A: Using compound angle formula &amp; trigonometric identities.

Q: If n is a positive integer greater than 1, then cos" udu = u sin u + n - 1 cos-1 cos" udu n-2 Use…

A: Given,          ∫excos5exdx

Q: Solve for O on Co, 2T) 6 sinio + 9 cos 0 -9-0 2 Sin O + 3cos o -3=0 Sin O +los? = Sm?O =1- cos?O…

A: Form the given trigonometric equation in the quadratic equation than solve by factorisation.

Q: ía) Given that z cos) + isino, show that z" + z" = 2cosn0 and z"- z" = 2isinno. Hence or otherwise,…

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Q: To evaluate sin 2x cos 2xdx conveniently, the formula/ identity to be used islare A None 1- cos4x…

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Q: 5 If sin u = 13 12 cosu = 13 3 and cos W = 5 W = --, find the exact value of each of the following:…

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Q: 94) Find the exact value Cos lutv) that 4=5 구 gven -3,4n Q1 and v in 03) tan and cos

A: Topic - trigonometric Identities

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

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Q: Which of the following is equivalent to cos (60° + 0) + sin(30° + 0)? cos 0 + v3 stn e cos e O…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.