Ou :? u =x +y +:, x=e" cos 21, y =e"21, : =e" = e" (cos 21-sin 4t +&t +8) +2e Ob. e (cos 21 - 2 sin 41 +8t +16r) +2e e" (cos' 21 -2cos 21 +4t+8 +2) Od. e" (sin2 21-2 sin 21 +4t+16r +2)

Q: Find formulas for the following general indefinite integrals to verify results (7), (8), and (10) in…

A: We’ll answer the 7th question since we answer only one question at a time. Please submit a new…

Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

A:

Q: Q4:B/Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: If +a= a(2 cos 0 cos 20) and y=a(2 sin0 sin 20),show that (z² + y² + 2az) = 4a² (z² + y²). %3D

A: Given that, x+a=a2cosθ-cos2θ⋯⋯1y=a2sinθ-sin2θ⋯⋯2 Squaring both sides of (1) and (2) and adding,…

Q: 2 1. (2{cos z = (2(com(금)+i sin())" ti sin( - 3 3 1+v3i 2.

A: Solution 1: Given 5∠π42 Here…

Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: = 0; y(0) = 2.2, y'(0) = -8.7, y"(0) = 38.85. O y = (91/150)sin 1.5t - 0.2cos 1.5t + 2.4e^(-4t) O y…

A:

Q: Show that 2 sin 0 + sin 20 sin 0 1- cos 20 1 cos e Prove that (G) 1 T 1 tan-1 + sin V5 3. where…

A:

Q: s nip

A: Given z=tanα2

Q: By using Cauchy laws find: sin (2) dz -i2 cos (2) dz 2-T3

A:

Q: Where are the theta valuss for the horizontal and vertical tangent lines on [0,2pi) of r=1+cos theta

A:

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 dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

A:

Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

A:

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

A:

Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

A:

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

A:

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: Suppose, z=-i+1.7 then, Find e-iz e(cos 1.7 +i sin 1.7) e(cos 1.7 - i sin 1.7) (cos 1.7 - i sin 1.7)…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1) y = 3sin(x) 2) y = 2sin(3x) 3) y = cos(-)

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: y cos?£ 1-CUSE tanzz

A:

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

Q: (i) Prove that sec 3x(sin 3x-2sin' 3x)= tan 3xcos 6x. (ii) Hence find, for 0s.xs, the values of x in…

A: Trigonometric equation

Q: An appropriate trigonometric substitution 1 -dx is V4 – x² for x = 2 tan(8) for 0 E (-5,5) а. b. x =…

A: The given integral is: ∫14-x2dx

Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

A:

Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

A:

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: Use Table to evaluate the following definite integrals.

A: The given integral is ∫0π40cos20xdx   formula used: ∫cosaxdx=1asinax+C

Q: The period of y = 3 cos 5x is 2 2 /5 2 /3

A: Given that: y=3cos5x

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: 19. 2 sin 3x = V2 %3D 21. 2 cos (2x + 1) = 1 23. 2 sin (4x - 1) = 1 3x 25. 2 cos %3D EN =

A: The give trigonometric equation is: 2sin3x=2    ....(1) As we know that if the trigonometric…

Q: Points of intersection Find the points of intersection of the circle r = 3 cos θ and the cardioid r…

A: Given:        r=3cosθ,   r=1+cosθ

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: express 5^(1/2) sin 2x + 2cos 2x =1 in the form R sin(2x + y) where R >0 and y is acute angle in…

A: Let's Solve,

Q: Why is V /5+ 5 tan² 0 = v5 sec² 0? Because Vtan 0 = sec 0 Because 1+ tan² 0 = sec² 0. • Because sec?…

A:

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

A:

Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A:

Q: sec 0 + In + 22+3 = -3 2 In y + 322-4 = 1+ cos 20 2/1+ (tan 0)2 +2ln y+2 3

A:

Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

A:

Q: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: B. - sin3 p cos 3p sin 3p cos 6p – sin 6p cos 6p H. sin 6p - cos 9p - sin 9p K cos 9p sin 9p LL

A:

Q: z1 = 30 (cos 20° +i sin 20°) and z2 = 6 (cos 5° + i sin 5") %3D %3D ( cos +i sin %3D

A:

Q: [cos 20-i sin20cos 30+ i sin301² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De Moivre's theorem?

A: We have to solve given Questions.

Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

A: