Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

Q: sin(x – y) cos x sin y tan x cot y – 1 Prove the identity:

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Q: 1-2sin? x 2. Prove cos x+ sin x +2sin cos-= cos x 2

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Q: 2. (a) only. Show the following using half angle or double angle identities sin z 1 (6) - COS I tan…

A: Given,  tanx2 = sinx1+cosx=1-cosxsinx  We have to prove the identities.

Q: Complete the identity. sin x coS X :? sin x cos X O A. sin xtan x O B. 1+ cot x OC. - 2tan x O D.…

A: Given

Q: Q:Prove that following identities: cos' B- cos A sin' A- sin' B cos B cos A cos' A cos B (1) tan'A-…

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Q: sin (x) tan(x) Vsec (x)-1 1-cos (x) Simplify the identity a) 2 b) 0 c) 1 d) 3

A: Using batch Trigonometric identities we can find the solution

Q: 6. Which is an identity equation? A. cos 2x B. tan 2x = -cot2 x C. cos 2x = cos? x- sin? x D. sin 2x…

A: 6). As we know the trigonometric identities: 1).…

Q: a) f(8) = -3 cos (e + ) + 2

A: The general form of a cosine function is y=acosbθ+c+d, where a, b, c, d are constants and a is the…

Q: 5 sin a -3 cos a 1 If 5 tan a = 4, Show that 5 sin a + 2 cos a 6

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Q: n sin A cos A 1-n sin? A If tan B prove tan(A – B)=(1–n)tan A.

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Q: Prove the identity. sin(x + y) – sin(x – y) = tan y cos(x - y) + cos(x + y) Use the Addition and…

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Q: 5(cos? z-1) sin z Cos I sin I

A: According to the trigonometric pythagorean identity, sin2x+cos2x=1 or cos2x-1=-sin2x or…

Q: 4.) Prove the identity. csc e Csc 20 2 cos e

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Q: lim z?e = Z→-3i %3D Select one: O a. 9 cos 9 cos 3 – 19 sin 3. O b. 9 cos 3 + 19 sin 3. c. -9 cos 3…

A: To evaluate the given limit

Q: 20. Which expression is equal to + tan x using identities? tan x cos a 1 sin a cos x 1 sin x sin x…

A: According to the tangent identity, tan x=sin xcos x. So, substitute tan x=sin xcos x in the…

Q: DI Ify x Sin x, x'sin x, .2 O a) 2 sin +x cos x O b) 2x sin x + x I SOƆ cos x O) 2x sinx - x cos x…

A: Use product rule of differentiation. D(uv) = D(u).v + u.D(v)

Q: Prove the identity. sin(x + y) – sin(x – y) - tan(y) cos(x + y) + cos(x - y) Use the Addition and…

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Q: 55. Verify the following identity and use it to give another proof of the formula (sin x)' = cos x:…

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Q: Which of the following is true? sin x dæ = - In | cos a+C tan x da = In cos a + C O DIn(tan x)] = 2…

A: Topic = Derivative and Integration All others are false only this is true ddxlntan x==2 csc 2x ⇒True…

Q: (ах) +k sin (az) kr +sin (ax) а cos Evaluate dæ e-

A: From the given problem: I=∫a cosax+ksinaxe-kx+sinaxdx As we know that; a-m=1am So, we can also write…

Q: Prove the following identity. (sin x – cos x)2 = 1 - sin 2x We begin by expanding the left side of…

A: Given : sinx - cosx2 = 1 - sin2x

Q: 6. Prove the following trigonometric identity. sin? x = cos x(sec x - cos x)

A: Find your answer below

Q: 2. Prove the identity: (1 + cot A - csc A)(1 + tan A + sec A) = 2

A: Write the trigonometric ratios in sinA and CosA.

Q: 1) prove the identity tan(A)sin(A) = sec(A) − cos(A)

A: We will use trigonometrical identity to find solution to the problem . According to bartleby…

Q: Which of the following are identities? - sin(-a) А. cos(-a) tan a B. sec 0 – sin 0 · tan 0 = cos 0…

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Q: complete the identity (sin x+cos x)^2 -1/ 2 sin x.cos x

A: sin^2 x+cos^2 x=1

Q: Recoll that e ošx Find S orecosx. 1/2 x sin(coi'x ) de

A: ∫012xsincos-1xdx

Q: 3 +6 sin x + 10 sinh h x dx = 3 cos-1 x-6 cos x- 10 coshx +c %3D True O False O 4 cot x dx =- cot x…

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Q: 12. Prove cach sin 0 + 2 cos 0 cos 0 + cos 0 es. a) sin 0 + 3 cos 0 - sin? 0 2 sin a - cos a tan a =…

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Q: 2. Prove each of the following identities: (a) sin x sin x cos? x = sinx Answer: (b) cos x/1-sin x…

A: Given identities  (A) sinx sinx cos2x=sin3x Put x=90° we get LSH=sin90° sin90° cos290°=0…

Q: De Moivre's formula (cos(0) + isin(0))- cos (0) + isn(0) 0 cos(no) + isin(no) ¤ COS infh

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Q: (ax) +k sin (ax) dx ka +sin (ax) а cos Evaluate e

A: On solving this integration we will get

Q: 1 12. Which expression is equal to + tan z using identities? tan z sin a cos a cos a 1 sin a cos e…

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Q: Which of these is a trig identity? sin x + cos x = 1 1/sin x = sec x sin(2x) = 2 sin x COS x tan x =…

A: Solution:From the following To find which of these is a trignometric identityFormula:tan x=sin xcos…

Q: We want to prove the identity; Cos r- Sin a Cos 2a. What is the first step in proving this? O Cos z…

A: We have to prove that cos4x-sin4x=cos2x We need to find the first step to prove this identity . We…

Q: 113. An Identity Involving Three Variables Suppose x = R cos 0 sin o, y = R sin 0 sin o, and z = R…

A: x=Rcosθsinϕ,  y=Rsinθsinϕ  &  z=Rcosϕ. Now consider,…

Q: Cos 0- sec 0 = sin 0 tan 0 Which of the following four statements shows the key steps in…

A: The inverse of trigonometric ratio cosine is given by secant i.e. cos(θ)=1sec(θ)   or…

Q: Verify the identity. 1 - cos(a) sin(a) 1 - cos(a) sin(a) sin(a) 1 + cos(a) 1- cos(a) sin(a) 1 1 +…

A: Given,…

Q: 25. The identity 2 sec? z has non-permissible values of: 1+ sin r 1- sin a Oz +an, n EI Ox ++an, nEI…

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Q: 2 sec? r 1 1 Prove the identity: 1-sin x + 1+sin x

A: This is trignomertric question

Q: v.' Verify the identity. 9.) cos x · cot x = csc x- sin x

A: Given: cosx·cotx=cscx-sinx   We know that the trigonometric identities; 1). sinx=1cscx 2).…

Q: Prove the identity. sin(x - y) – sin(x + y) = cos(x + y) + cos(x- y) -tan(y) Use the Addition and…

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Q: 5 sin a - 3 cos a 1 If 5 tan a = 4, show that 5 sin a +2 cos a 6.

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Q: Which of the following are identities? sin x 1- cos z 1+ cos x sin x 1- sin x cos x II. 1+ sin x cos…

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Q: p(x) = sin cos x Select the correct response: tan x O 1 O sin? x – cos² x 2 COS“ x -

A: Given that

Q: 20. A certain substitution gives S sin³x cos"x dx = S (u° - u’) du . What is n? Your answer

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Q: Prove that the following identity is true. tan x sin? x + sin x cos X sin x - cos x COS X cos x - 2…

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Q: erify the following identities: 1-sin(x) 1-sin(x) %3D V1+sin(x) |cos(x)| sin*(x). cos?(x) = cos?(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.