1) z = 6| cos 3T +i sin 2 +i sin 6 W = 12] COS 6 Find 2.

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

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

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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: cos 20 = 3 sin 0 – 1 (1 – 2sin?0) – 3 sin 0 + 1 = 0 2 sin? 0 + 3 sin 0 – 2 = 0

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Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

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Q: 5х, 5x sin°(cos* () dx 5 4 6 6

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Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: cos 2x + 2 sin 2 x = _______

A: This question can be solved by applying the formula of cos2x cos2x=cos2x-sin2x

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

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Q: 1 sinx # 1-cos2x ẩu! (6 2

A: Given query is to find the value of the limit.

Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

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Q: 5. (sin 0 – 2r cos² 0) dr + r cos 0 (2r sin 0 + 1) d0 = 0

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

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Q: 25. y = 2 cos yA 2 28. y = 2 sin ) -2TT -2 31. y = 3 sin (2x) (A)

A: In this, the amplitude is multiplied by 2 and x is scaled by 1/2.

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: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: Express f (0) = cos 20 + 4(sin 20)² + 1 as a sum of powers of sin 0.

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Q: 8. 5 cos²x - 3tan x COS X dx

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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: 2) Find all solution of the equations in the interval [0,2x]. a) 2sin 30+ 12 = 0 b) (cosx- 1)(sin x…

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Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: 3. 2 [sin 4 3x cos² 3xdx

A: 3. To evaluate the ∫sin43x cos23x dxFormula: (1) cos2x=1-sin2x(2) ∫sinn xdx=-1n sinn-1x cos x+n-1n…

Q: Cos(5x) cos(2x) + sin(5x) sin(2x)

A: Given: Cos(5x) cos(2x) + sin(5x) sin(2x)

Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

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: 13T (b) sin-(sin(- -)) = %3D 11

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Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

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Q: dr 5) J, (2z– 1)3/2 (2x – 1)3/2 4 cos( sin2( dr

A: Integration is the process of finding the anti-derivative function of the given function.…

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

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Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: sin 2t cos 2t dt 1 +3 cos 4t

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: 3. sin(2x - 6) = cos(4x + 18) %3D

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

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Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

Q: 3 3m 2. sin ---- sin(20) = b. cos(20) = a.

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

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Q: 11. One leaf of r = cos 30 12. One leaf of r = sin 40 13. Bounded by r = 2 cose %3D 14. Bounded by r…

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Q: 1) B = cos 30 + sin² 0 tan 2x 2) y = 1-cot 2x 3) w = 2 csc(1 – 3x)

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: do 6) I cos° 0 7 [(1- sin° 31)- cos3t dt 8) | tan (5x)· sec (5x) dx

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

Q: 4 2 cos y + sen²y cos² y - senty 3 cos² y 1

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

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Q: 1. у%3 Sin 5x +1 2. y = cos 3. у 3 tan (7x-1)

A: 1st derivative of 1st 3 trigonometric function are :

Q: 1. Solve the DE: tan xsin y y'+(3 tan x-2 cos y) secx= 0

A: Given tanxsinyy'+3tanx-2cosysec2x =0 tanxsinydydx+3tanx-2cosysec2x =0 3tanx-2cosysec2xdx+tanxsinydy…

Q: 23, sin 50° + sin 40° 23. sin A VZ cos 5° B 2 cos 10° 2 cos 5° D V2 cos 10°

A: Trigonometric identity: sin x+sin y=2sinx+y2cosx-y2

Q: (7) (4+sin-15x)° dx V1-25x2 3. dx (8) J Ja +x Vx

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.