Let t be the angle between 0 and such that sin t Then cos t sin(-t) cos(-t) tant =

Q: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

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Q: Tan Be Xe O de d Bo find

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Q: Let p be the circular function that sends a real number A to the point (cos 0, sin 6). If P(0) = (x,…

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Q: Use the Fundamental Theorem of Calculus to find (2 + cos x) dx.

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Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y) = sin y %3D

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Q: Assume that sin u = 3/5 and sin v = 4/5. Find cos (u - v). I need all work.

A: Given:

Q: If f(z) = 2 sin I +3 cos z, then f'(x) = %3D

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Q: O1) Prove that: [Answer only two du dx (A) - tanh u = dx 1-u du (B) u-1 = sec u+C >1 2. (C) cscx =…

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Q: tan z, + tanz, = T-(tan z;) +(tan 72) tan(z, +2) ) Prove that: cos(z + w) = cosz cosw + sinz sin w

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Q: B. If sin u = tan u < 0, find : 1. sin u/2 2. cos u/2 3. tan u/2

A: Given that, sinu=tanu&lt;0

Q: Let the position vcctor bc R CE) = <3€,2 cos (3€), 2 sin (3€) Compute the curuature

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Q: Let y = tan10 (x5).Find ƒ, g, and h such that y = ƒ(u),where u = g(v) and v = h(x).

A: The given function is

Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: Find the function if sin t T+1 1 tan 2x + 1

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Q: Prove the identity. sin(x+y) sinx + cos(x+y) cosx = cosy

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Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: Prove the trigonometric identity. tan t cot z sec z

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Q: Find sin(u+v) given the following information. cos u= -4/5, π ≤ u ≤ 3π/2 tan v=-5/8, 3π/2 ≤ v ≤ 2π

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

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

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Q: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: Prove that sin (x +y) sin (x - y) tan x + tan y) %3D tan x – tan y

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Q: 21. dridt + r tan t = cos? t, r(T/3) = 1 Answer: r= cos t( sin t+ 2 - V3/2)

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Q: Let - (sin x cos y, COS I sin y, In). Compute div i

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Q: ha)= Jo So Sin't dt

A: We have to find the given integral .

Q: Prove the following identities. sin(u – v) 12. = cotv-cotu sinu sinv

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Q: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: Consider the function defined by f(z) = sin z cos 3z. Find f" () Give an exact answer.

A: We know that, product rule of differentiation states that ddxfx·gx=fx·g'x+gx·f'x            ⋯⋯1 We…

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: verify the following trignometric identities. 2cos xsin y = sin (x+y) - sin(x-y)

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Q: (2 cos t, 2 sin t, t), where 0 <t < .

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Q: Let r(t) = (sin 3r, cos 3r, /īt), Find T(t) and N(t)

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: Evaluate: sin z dz +(°z – z)

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Q: Prove that cos (÷+t) = - sin t

A: We have to prove that cos(π\2 + t) = -sint

Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Let z = r+iy, r, y E R. Show that if cos a = 0, then cosh y cosh y 1 <1. | cot 2|2 :

A: Let z=x+iy, x,y∈R. Consider cos x=0. And we know that cot z=cos zsin z

Q: sin(x + y) – sin(x – y) = 2 cos x sin y

A: sinx+y-sinx-y=sinx cosy+cosx siny-sinx cosy-cosx siny=sinx cosy+cosx siny-sinx cosy+cosx siny=cosx…

Q: Consider the function defined by f(z) sin z cos 3z. %3D Find f" () . Give an exact answer.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Prove that: sin(z + w) = sin z cos w +

A: Here we have to prove that,

Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: Verify the identity sin t cos t(tan t + cot t) = 1.

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Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz

Q: 4) Sin W = %3D Cos N = W. Tan W = %3D

A: Solution: The objective is to find the required values

Q: Find cos(u – v) given the following information. 4 sin u = 5' 3 2 1 sin v = 3' 2

A: As per the company guidelines we can solve first question. I hope that the given solution will help…