When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of the following is U' ? -sin2x U' = A 2cos2x sin2x U' = cos²2x B sin²2x U' = 2cos2x U' =tan2x %3D

Q: 2 cos(0) and 0 satisfies 0 < 0 < find si 2' in(0) %3D

A:

Q: If /n= ( 5x + 9 )" sinx dx , Then I,+25n(n-1) In-2=. Select one: O - ( 5x + 9 )" cosx + 5n ( 5x + 9…

A:

Q: cos( 2 sin1 (X/17)) = Select one: O 2x ( 289 - x )o./ 289 O ( 2x - 289 )/289 None O 34 x/( 289 + x)…

A:

Q: Prove the following trigonometric identities. 1 cotx a) 6 cosx| 6 cosx = 6sin² x COSX CSCX

A: The details solution is given below

Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Solve x 2x 2x 2π cos - ( 2² -1) + sin ~¹ ( 24₁ ) + tan - ( ²²₁ ) = ² COS 2 +1 x +1 3 -

A:

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

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Q: 15(- + 16.5 2 = 15 cos 15 + 16.5 = 15 cos y = y = |

A: The first function is: y=15cosπ15t-π2+16.5 Second function is: y=15cosπ15t-152+16.5

Q: cscx−sinx cos²x CSC X =

A: We need to prove that cscx-sinxcscx=cos2x

Q: 1-) 2csc23x 1-S sec3xVsin3x

A:

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: If y = sin 2x sin 3x sin 4x then find y".

A:

Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

A:

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: 2) y = sin(3x²ex)

A: Find the derivative

Q: If 4 f(x) = %3D 1+ sin x then 4 cos x f'(x) = (1 + sin x)²

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.