Find cos Co + u given that COs o =) se3z and cos =3. and that & and 4 are between O and /2.

Q: Find the product of zı and z2 Given zı = 4 (cos 180 ° + i sin 180 °) and Z2 = 4 (cos 145° + i sin…

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Q: H.co/prove That;- CoS z

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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: - 1, z = cos-

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Q: 6/155) cos 0, 1+ cos 29

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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: We have 27 Cos (u) du= and converting back to an expression in X qrues us

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Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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

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Q: Find θ with 0 ≤ θ < 2π and cosθ=−3–√2

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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: If sin u  = 3/ 5 and sin v = 4/5  and that u and v  are  between  0 and π/2,   evaluate :     cos (…

A: given: sinu=35 sinv=45 and u and v are between 0 and π2. we have to evaluate cos(u-v)

Q: Use the product-to-sum identity 2 cos A cos B = cos (A + B) + cos (A – B) to prove the sum-to- P +…

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Q: find cos(u/2) if cos u = 0.229 and u is in quadrant 1 cos (u/2) = ?

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

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Q: Show thatI cos ve (-1/4s)

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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: 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: cos" xdx :0. 6. If n is a positive odd integer, prove that

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

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Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

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Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

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Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

Q: Prove that there exists a value of x so that -1 COS T = cosx %3D ned to

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Q: Compute cos (2). As a helpful comment, notice that 4. 4 O V3+v2 || kko

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Q: Show that: cos z=0 if and only if z (/2) + kT.

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Compute cos (cos-1(3/2)) O 3/2 O This quantity does not exist.

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Q: Find the points of intersection of r = 1 andr = 1+2 cos 0.

A: General solution of cosθ = cosα is                           θ = 2nπ ±α

Q: For θ between 0° and 360°, find the two values of θ that satisfy the following.  cos θ = √2/2

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Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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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: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

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

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Q: inside 2 = 2 cos 20 and outside r = 1

A: We have to find area between the polar curve.

Q: 4) Find the exactvalue coslu+v) that tan and cos v 3 in Q1, and Vin Q3) 7

A: Question is solved.

Q: Show that: cos z= 0 if and only if z (/2)+ kT.

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Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

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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: Find   cos(u/2)   if   sec u=7.519

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Q: E. Prove. 1+ cos20 – cos²0 = cos20 %3D

A: To prove:- 1+cos(2θ)-cos2(θ)=cos2(θ)

Q: Use the addition formula to prove                                                             cos 3θ…

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: If tan A =ntan B and Sin A :m sin B. psove that co s A: m²-1 2.

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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…

Q: Q6:- Prove that: y" = 0 if (cos y3csc COS

A: To prove : y'' =0

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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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.