3 Show that sin"0= 8 2 1 cos (20) + cos (40). 8 Which of the following four statements establishes the identity? OA. sin *0= ( sin 1+ cos (20)) 3 ²0)² = 1 cos (20) + 1 cos (40) %3D 2 8 O B. sin *o= ( sin*o)° = 1- cos (20) 3 1 %3D 8. cos (20) + cos (40) 8 C. sin *0= ( sin20)= 1+ cos (20) 3 1 1. 2. 8 2 cos (20) + cos (40) O D. sin*o= ( sin²o)* = cos (20) 3 cos (20) + 1 cos (40) 2 8 21 2.

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Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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

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Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

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Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

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Q: 19. sin' 0.3 od ni be 20. sin 0.47 21. sin (-0.32) -1 STS 22. sin (-0.625) -14 24. cos -1 23. cos 8.…

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Q: 12 Prove that sin 80 cos 0-sin 60 cos 30 a. = tan 20 cos 20 cos 0- sin 30 sin 40

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

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: Q1. Simplify (cos-isin )² (cos 70+isin 70)-³ (cos 40+ i sin 40)² (cos+ i sin 0)³ using De Movier's…

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Q: Which of the followings are false? I. General term of {2,3,2,3,...} is an =;+(-)". . General term of…

A: The details solution is given bellow.

Q: Can you show me a step-by-step proof

A: We need the following two identities to produce the required prove:

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: 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: 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) do -(1-cos a). 2 ||

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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Q: 4 81-72sin²0+16sin*6 do S sin 20 de 1–2cos²0+cos40

A: Let…

Q: 9-simplify sin 3π/4 сos π/3 +cos 3π/3 sin π/3 a) Sin 13π/12 b) Sin 5π/12 c) Cos 13/12 d) Cos 5π/12

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Q: 3 Show that sin' 0 cos“ 0 1 1 cos (40) + 32 cos 128 cos ( 80). 128

A: To prove that,           sin4θcos4θ=3128-132cos4θ+1128cos8θ

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A: The solution is :

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: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

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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: 4 Giren tan A =– where 0<AS Find 2sin 2A.

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Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

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Q: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

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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: 5. Evaluate | 3 ( cos 45°+ isin 45°) using De Moivre's Theorem.

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Q: 2 2 Establish the identity sec 1+ cos 0 Which of the following four statements establishes the…

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

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Q: 3 Show that sin 0: 8. 1 cos (20) + %3D cos (40). 8 Which of the following four statements…

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

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Q: The simplified form of cos ( - 12a) + sin (* + - 12=) 6 O v2 cos 12r + 2 sin 12x O V3 cos 12a + v2…

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

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Q: 40. Show that cos(30) = 4 cos e - 3 cos e for all 0. [Hint: cos(30) = cos(20 + 0).]

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Q: Find the root (7 – 7i)/2 O +7/2[cos(x/4) – isin(x/4)] O +V98[cos(r/8) – isin(x/8)] O +7/2[cos(x/8) +…

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

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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…

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Q: 1 cos 20 cos² 20 8. Prove: cos* 0==+ 4 4

A: