If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

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Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

Q: Differentiate. cosx² + siny³ = 36 %3D

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Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: find the value of cE CoB] for flx)= that satisfy value theorem. mean

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Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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

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Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: Find 19. t sin 3t dt Jo

A: Topic:- integration  Note:- as per our guideline if more than one question uploaded than only first…

Q: Calculate fsin³ a cos° a dx.

A: Let cosx = t Differentiate on both side   - sinx. dx = dt    sinx. dx =  - dt

Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

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: Find the first 3 Zerms o Sinx et a =?

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Q: Use linear approximations to estimate the following. 1. sin 9/4

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Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: Compute : exp(i sin(e-i))

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Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

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Q: cos 2x +1 sm 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: We know the formula (1) 1+cos(2x)=2cos2x (2) 1-cos(2x)=2sin2x (3) sin(2x)=2sinxcosx

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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

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Q: If Z= sinh () x- show that:

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Q: use Eq. (8) to find dy/dx at the given point.  (sin 2θ , cos 3θ ), θ = π/6

A: Solution:Given   (sin2θ, cos3θ),     θ=π6To find dydxFormula:ddxsin θ=cosθddxcos θ=-sin θ

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: 1- -In2 - cosh? () . 2 - cosh(Inx) dx

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

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same time) 1.…

A: sin2x=1-cos2x and,  tanx= sin(x)/cos(x)

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: Compute sin (3r)dr (25z4+1)2 -

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Q: Show that cos(arcsinx) Vi - x², for x| s lin two different ways.

A: Show that cosarcsin(x)=1-x2, for x≤1

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

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Q: Derve the Jrmula Cosh 2. Find dy Sor Sin ソー X-/ xp

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Q: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: Let fla)= é cosx, s** %3D Express your answers in exact form.

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Q: Left in implicit form

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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Q: E prove that - Cotx + C 2 |- Cosx +Sinx

A: Solve the integration

Q: Suppose that sin(In z) = }, and that sin(In y) = }. If 0 < In z < and 0 < In y < §, use the…

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Q: S- cos ve ve sin? ve de =

A: We will evaluate the given integral.

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.