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Q: b. Prove that 2cot (20) = cot(0) - tan(0)

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Q: Prove the following  (sinx)(secx)(cotx)= 1

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Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

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Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: tan u du = In | sec u| + C

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Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

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

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Q: . Evaluate sec z tan zdr

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Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

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Q: a) Show that: tan z, + tan z, tan(z, + 2) = 1- (tan z) +(tan z)

A: To prove the formula:

Q: Q. Use first principle rule and proue that if y=s %3D secl tand = secx

A: Given: y=secx We know that for any given functiony=fx, first derivative is given by…

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: prove the followi Sin(zy) 1-Cos (zy) identity ng tancy)

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Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: Find the areg between Ye CosX an d y--SinX trom o tr .

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Q: కషిద్టి చవీ / tangent s lope rosin (20) when Jot 5 2) 653 3. not of the above

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Q: esirq) . cos(q) dq 5x/2

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Q: find: de So 2-cose using sediment theorem

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Q: secx tanx :1 cosx cotx

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Q: If Y=tanx prove that %3D2

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Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

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Q: prove that. sinh ciz) = i sinz sinciz) zisinh z , cescia)= coshz

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Q: Find if r = sin[cos(-0)]. de dr = sin 0 cos(cos 0) de dr cos[sin(-0)] de Option 3 Option 1 dr dr sin…

A: This question is based on application of Derivative.

Q: How: e way, prove that By the sam e 王Sinw.k sin Wok

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Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

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Q: Exercise 3. Show that (a) sin z = sin z: (b) cos z = cos 7.

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Q: Integrate sin" uelor (cosu) . Where n=540

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Q: Show that cos( arctan( sin( arccot(x)))) = sqrt{{x^2+1}/{x^2+2}}

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Q: HW /Prove that: (1) tanx=cot

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

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0,1 )

A: Concept: Trignometry inverse formula: One of the key ideas in mathematics is the inverse…

Q: HW/ Prove that: (1) 1-tanif x sechx

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Q: Prove the following 1/tanx+cotx=sinxcosx

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Q: -Prove that: y" = 1 if y=csc(tan")

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Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: Let slx) = tan X %3D 3, ind ) tanx dx using Lebesgue in tegral.

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Q: Prove that? 2tanX tan 2X %3D 2 1- tan x

A: Given : 2tanx1-tan2x = tan2x

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Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

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Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: Integrate sin®19uelog (cosu)

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Q: Prove that arcsin x = arctan , [지 < 1. 1 – x

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Q: Prove that _ d tanx = Sec'x.

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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.