(4) Use diffential equations to prove the trig identity sin(r + a) = sin(r) cos(a) = sin(a) cos(x) %3D %3D

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Q: a. Express x = -3+52 in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: Given:  a) x=-3+5i Any complex number z=a+bi  has a trigonometric form  x=rcosθ+isinθ where…

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A: We are given trigonometric equation as

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Q: 3 sin x dx 3. | COs cos? x

A: Our Aim is to solve the integral given below:-I=∫sin3 (x)cos2 (x)dx -(i)

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Q: COS X 1. S 7+cos 2x

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Q: (a) Find S(tan x)dx (b) Evaluate i sin 3x cos 3x dx d (c) Find (2x sin 2x + cos 2x) and hence…

A: a) ∫tan2πx dxb) ∫π9π6sin3x cos3x dxc) ddx2xsin2x+cos2x and ∫0π4x cos2xdx

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A: We have to find the value of B in the given question.  This question can be done by using…

Q: Establish each identity given in attachment.

A: Given equation: asinθ+bcosθ2+acosθ-bsinθ2=a2+b2

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Q: 2 + sin x Differentiate Y x + cos

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Q: 1- cos A + sin A -then 2 sin A If y = is equal to 1+ cos A + sin A 1+ sin A

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Q: ·S- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: The given integral is ∫x dxx2+x2-1-1. We have to change the integral using substitution.

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A: Let's transform integral by using trigonometric substitution.

Q: sin x dx cos? x + cos x 23.

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Q: sin 2x (a – b 2x)4 + K. VI Cos 2r

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Q: A. Bernoulli's Egquation 2. (3 tan X - 2 cos y) sec?xdx + tan x sin ydy - 0

A: Explanation The equation is in the form dydx+P(x)y=Q(x)yn is called the Bernoulli's equation Now we…

Q: 7a/4 Evaluate the integral (sin x+ cos x) dx using the fundamental theorem of calculus. Discuss…

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Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

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A: First we show that given differential equation is exact then we solve  for exact differential…

Q: Sంబు ఒపా వింద ఇ + పిల్లయ 2-Sin LA Sin A tos A Sin A t cOS A 0.

A: Given : (2sin³A + 2cos³A)/(sinA + cosA) = 2 - sin2A

Q: 37. 2(cos x)-/2 sin x dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

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Q: A. Using trigonometric identities 1. S sin53x(cos 3x)-2/5dx 2. S cot5 2x csc-4 2x dx

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Q: 2sina 1 - cosa + sin& If 1+ cosa + sina = x, then %3D 1 + sinɑ (A) ! (B) x (C) 1 -x (D) 1 + x

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Q: (7) csc (2.x + 1) cot(2x + 1) dx CSC' sin 0 cos 0 cos(cos 20) de

A: We will solve the problem

Q: 10. Evaluate. (d) sin-1() (e) sin¬1 (sin (7)) (f) sin- (cos (E) (a) sin-' (0) (b) cos-1 (-) (c)…

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Q: Question 20 sin (x) Evaluate: dx sin(x) +1 1- sin(x) (A) cos(x) +x+C 1+ sin(x) B cos(x) -- x+C cos…

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Q: Cos A +1+ sin A 2 sec A 1+ sin A %3D cos A

A: To Prove: cosA1+sinA+1+sinAcosA=2secA

Q: Find each determinant.

A: a).

Q: x2 cos x 6. Find for y = ln: dx sec x а. 2x – sin x – tan x sec x b. + cot x - tan x 2 cot x – tan x…

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Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: sin ф dp cos? ф 4x 3x + cos (2x² + 1)| dx tan? x (1+ sin“ x) dr cos².

A: Note: as per our guidelines we are supposed to answer only one question if there are multiple…

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Q: HW: (1) Prove that: cos'e (a) 1- tan'e 1-cot' @ sin'e -1, (b) tan'0.cos' 0 + cot³ 0.sin³ 0 -1

A: The detailed solution is as follows below:

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Q: 1. [sin x cos 8.xdr

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Q: 8]. r = sin 0 -2 cos 0

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Q: a) I = § sin (x) dx %3D b) I = J cos5 (x) sin² (x) dx

A: ∫sin7x dxsin2x=1-cos2x∫sin6x ·sinx  dx∫sin2x3 ·sinx  dx∫1-cos2x3 ·sinx  dxlet u=cosxdu=-sinx…

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Q: (* sin - 2y cos )d = 0. dr+2ry cosdy COS

A: Find the attachment

Q: cos 2x+sin? x 1.4 a) Prove the identity: =1- sin x. 1+ sin x

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