b. Given that z = el®, show that z" += 2 cos ne. Hence, show that cos 50 = 16 sint 0 – 112 sin² 0 + 1, cos e for cos 0 + 0.

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

A: Introduction :

Q: Which of the following is equivalent to | cos(4a)sin (4x) da ? cos udu · 1 sin udu, where u = 4x…

A: The answer is found in step-2.

Q: 3 with A e QIII , find sin2A 8 7. If cos A =--

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

Q: A-Show that S 1, L{cos at} s2+a²

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

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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

A:

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…

A:

Q: 3. Let sin A = with A in QII and cos B = – -i with B in QIII. Find cos(A+ B). (4pts)

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Q: A periodic signal is given by r(t) = 3 cos(t) + cos (5t 2n - 2 sin (8t + 3

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Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

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: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

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Q: 2). Express the following : > 20° in radians. T/9 rad in degree. 2b). prove that: (sinø-cosø)^2 +…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this…

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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: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

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Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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

A: Follow the steps.

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

A:

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

Q: 4. Evaluate the following and give the exact value: - Tt/4 r2 cos 0 crsin 0 r2 cos 0 dz dr d0 0,

A:

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

A:

Q: The integral So (cos(3x))² sin(3x)dx under the change of variable u = cos3x becomes - ov 29 9/29 u?…

A:

Q: Let sin A = - with 270° SAS360 and cos B% = 24 25 sin(A + B) 4/5

A: The given values are Now, to find the value of sin(A+B), use formula

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: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: 5 1. If sec a with a in quadrant Il and cos B = with B in quadrant IV evaluate: 3 a) sin(a- B) b)…

A: If sec α=-52 with α in quadrant II and cos β=13 with β in quadrant IV, then to evaluate the…

Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

A:

Q: 1 tan z = 3'

A: The value of tanz =13  is given where, π≤z≤3π2 Solution: (a) Now  we have ,tanz =13, So -tanz will…

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

A:

Q: Show that the following equation [ has a solution on (0, 2). 42-1 = πX 2 5 cos(-

A: The given equation,       4x-1=5cosπx2

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

A:

Q: Find cos (0 + p) given that cos 0 = 2 and cos p = 2 and that 0 and p are between 0 and t/2.

A: For the given values of  Cos(θ)=1213 Cos (ϕ) = 35 Cos(θ+ϕ ) is evaluated as shown below

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: 17. Choose the best answer. (- - ) Ifain ( - ). cos z and sin 3 find cos 2 2 1 2 V3 2

A: Here we have to find the value of cos(pi/6).

Q: b. cos(3n) + 2 sin(3n)

A: Solution :-

Q: Find the values of z satisfying cos Az = 0 2

A: Result : General Solution of  cosx=0 is x=(2n+1)π2

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

A: The given trignometric equation is2cosθ+2 =0

Q: Find cos (0 + p) given that cos 0 = and cos p = and that 0 and p are %3D between 0 and n/2.

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Q: 2)50lve For Oso<27 -13 Sin n a =Coso

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: 7) Given that tan(a) = with a in QIII and cot(B) = --with B in QIV, find sin(a +B) and cos(2a). %3D…

A: Given : tan(α)=23 with α in QIII and cot(β)=-14 with β in QIV. The objective is to find the value of…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.