1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n + 1)a – tan a]

Q: ſcos 3t sin 8t dt * 1/2 (-1/5 cos5t - 1/11 cos11t ) + C O 1/2 (1/5 cos5t - 1/11 cos11t) + C O None…

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Q: 3.4 Find the residue of f(2) = (1 – 2º) sin(1/2).

A: Find the residue of f(z)=(1-z^6)sin(1/z) We know that residue of f(z) is the coefficient of (1/z) in…

Q: 23. Find all solutions of cos r = exactly that exist on the interval 0, 27)

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Q: 2. 3- va(c + ian ) - va(0+ in ) Z1 = + i sin + i sin COs 22 = cos

A: This is the problem of complex analysis.

Q: 3.7 O cos ) cos(8-x) cos - cos 3

A:

Q: 1 = 1 +x+x?+ 1-x Ex", I지<1 n=0 1 = 1-x+x2- ... + (-x)"+ 1+x E(-1)"x", x|<1 n=0 x2 ex = 1+x+ 2! x"…

A: use e^x expension

Q: 2 WWw -21 2T -TT TT -2 -4 -6 s(2) = 3sin(x + )-2 f(x) = 3 sin x + 4 A) f(x) = 3 sin 2x + -2 B) f (x)…

A: Please go through the attached solution.  Thankyou . Best regards.

Q: -2 a -1 23 1 b-a 2 1 4 T -cos³x sin ²x 1 -2 - e b+ a e 3-b - 1 2 NO - 1 1 -1 O 2 1 013 4 1 خدم برد…

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Q: establish each identity

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

Q: 2. an = 3 +- + cos(2nz) п 3. an = In(14n – n) – In(3n° + 2n² + 1) - |

A:

Q: In Exercises 7–12, one of sin x, cos x, and tan x is given. Find the other two if x lies in the…

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

Q: If Z-1/v2+i/v2 then the value of conjugate of Z^5=?* O cos(3n/4) O 2sin(5n/4) O 2cos(5n/4) cos(5n/4)

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Q: 1 0 x' = 6 1 -6 |x 4 6 1 X = c1 -4 e + c2e'| cos 61 + c3e' sin 61 6. sin 61 - cos 61 6. -4 e' + c2e…

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Q: = 15 - 3e-2t cos 3.464t - 1.732 e-2tsin 3.464t v(e) %3D

A: Find your answer below

Q: 2/2 16/1+cos 0 de 0

A: We use the half-angle identity

Q: f3(x) = 3 x',32 - 2, fa(x) = 5x² cos(x)+ 7VT. 212 + x – 1 fs(x) = 8 sen[2(x – 3)5 + 1], fe(x) %3D x²…

A: According to our guidelines we can answer only three subparts and rest can be reposted. f5 is wrong.…

Q: 3.4 Find the residue of f(2) = (1 – 26) sin(1/2).

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Q: .z² = cos(1 + i) .z² = In(1+i)

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Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

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

A:

Q: where do these (encircled in red) come from?

A: I am attaching image so that you understand each and every step. Please take exact value then we get…

Q: 3-26 · Evaluate the integral. 3. (x cos 5x dx

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Q: 5. Find ALL degree solution of 3sin 0 + 3 = 2 cos' 0.

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Q: sin k 1-cos 2k 24. 9. 36sin k

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Q: 3 65 7.Secnario-1: cos" + sin +cos ec 13 5 16 Secnario-2: f(x)= tan x. 1-x² a) Show that 2 tanx =…

A: Given,cos-135+sin-1513+cosec-16516and fx=tan x

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: 5) 2√√3 cos sin 0 - cos 0 = 2cos 0

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

A:

Q: Express as a product a. cos 5t + cos 6t b. cos x + 2x

A: We have to express as a product  (a)  Cos 5t + Cos 6t We know that  CosC + CosD =…

Q: 1. Express as a sum or difference a.) sin 7t sin t b.) cos 6u cos (-4u) c.) cos 2t sin 6t d.) 2…

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Q: 3. Show f cos2n Ode 277 sin-n Ꮎ ᏧᎾ = 27 22n 11.1 n = 1, 2, 3,...

A: Using Cauchy integral formula.

Q: 1+ cos(8) sin(8) 2 csc(0) sin(0) 1 + cos(0) 1 + cos(8) D + sin?c®) sin(0) sin(0) 1+ cos(0) sin(0)(1…

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Q: 1 1 COS COS | n² (n + 1)² n=1

A: We will find out the required value.

Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13

Q: 21 +2.T.0 () +2-т-0 3 • k = 0: V512 ( cos 2 (cos (-) (–)) = 2 cos () – 2i sin () + i sin 3 COS 9. +…

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Q: 2/2 00 (-1)" (2n + 1)³' COs nx 1°) Show that dr = Justify your reasoning. n=1

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Q: 3) [~x cos² (x3/2 - 8) dx , A)sin (x/2 - 8) + C 1 = x3/2 – 8 3) 1 B) a32 - 8) + sin 2432 - 8) • C D)…

A:

Q: 1 cos Cos (n + 1)² n n=1

A: A telescoping series is any series where nearly every term cancels with a preceeding or following…

Q: 18) tan 3x 24) 2sin? 0 3(1-cos 0) 4 25) sin (20)= co cos O 19) cos-x X- cot 26) 4 cos B = 1 + 4sin B…

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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: 5. lim(2' – 1) cos = 0

A: we know the standard limits s.t  limt→0ax-1x=loga

Q: (2n + 1)п' 4 sin =? (2n + 1) n=0

A: The given series is: ∑n=0∞sin(2n+1)π4(2n+1)

Q: 2csc 0--cos Ocsc 0 + cos 0+2csc 0 a 5x Sa 7a A) 4 3 4 3n B) 0, 4 7x 4 T 37 C) 2 2 3 5x D) 2 3

A: cosθ=0 implies θ= (2n-1)π/2 , n is any integer. cscθ= 1 implies, θ=(4n+1)π/2 , n is any integer.

Q: 7.3.1. Determine cos A for A = ( 2). -T/2 T/2 T/2 -T/2

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Q: 1n 1-Co1 2n

A: To evaluate ∫π4π2 sin 2x1 - cos 2x dx

Q: (-1)"2x2n+1 2n +1 1. n=0 2x2n+1 2. (-1)". (2n + 1)! n=0 (-1)*2²" x2n (2n)! 3. n=0 2" x" 4. n! n=0 A.…

A: According to question "we have to choose the Maclaurin serieswith correct function correctly"

Q: 1 - T <x< T Ans. 4 cos(x) +cos(2.x) - 4 1 ***+ (xɛ)soɔ- 4) f(x) = 12

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Q: 2n (1-cos0 5. Evaluate p³cos²0 dpd0

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.