Show that a. cosh iu = cos u, b. sinh iu = i sin u.

Q: E valuate sin" e cae de

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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: Compute : exp(i sin(e¬ni)).

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Q: Find tue indefinike insegred. Jcostex) sin'ces) de 3 6 (os (2x) Sin

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Q: If L--in a/a¢, then [L,cosø ] = iħsino I O iħsin20 .II O iħcoso .III O

A: It is given that Lz⏞=-in∂∂ϕ,

Q: Let 3 sin z+ 6 cos y= 4.

A: The first derivative of y with respect to x is given by the expression . The second derivative of y…

Q: 3 Select the angles with a tangent ratio of 4 ZA ZE

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Q: If sinh z = , then coth z is

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Q: Calculate du. u = cos(x2)

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Q: Evaluate the integrals

A: Consider the integrals 31)    ∫0π/27costsintdt32)    ∫0π/413tantsec2tdt

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 crea trom X = 0 to 2 rad y=2 sin '/2 Tr x.

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

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Q: 177 Give the exact value of Cot

A: You must have the idea of basic trigonometric formula.

Q: Calculate fsin³ a cos° a dx.

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

Q: Evaluate fi' sin(21*)dt

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Q: 1)cotx will be cont 0) is

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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: tan (x) = 7.1. If x and y are complementary, what is cot (y)? %3D

A: Given,          tanx=7.1 . If x and y are complementary.

Q: (a) Evaluate by parts: |x cos4xdx

A: In this question we have to find solution by using Integration by parts.

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

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Q: Prove the identity. cotx cosx+ sınx CSCX

A: The objective is to prove the identity.

Q: What is the value of the i in the ex

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

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Q: cos(Inɔx),>o

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Q: Evaluate: sin z -dz +(°z – z)

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Q: Show that the following statement is true by transforming theleft side into the right side. cos…

A: We have to prove the statement: cos θ tan θ=sin θ We know that tan θ=sin θcos θ

Q: sinha da 1+cosha

A: ∫sinhω1+coshωdωLet u=1+coshω.=∫1udu=lnuSubstitute back u=1+coshω=ln1+coshωAdd a constant to the…

Q: If cos u = - 2/3and u terminates in QIII, find sin u.

A: Given: cosu=-23, u terminates in 3rd quadrant We know that if u is in 3rd quadrant then sinu and…

Q: Show that sinh iθ = i sin θ.

A: Given:sinh iθ=i sinθ

Q: Verify the identity. cos(u+v) +cos(u−v) = 2cosucosv

A: The given equation to be verified is: cosu+v+cosu-v=2cosu cosv  The identity cosu+v is : cosu+v=cosu…

Q: Express rad in degrees.

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Q: We have - (cos (u) du=

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Q: Find the concevity. point of infleetion, of fluj n=770 Also explain it jeometrically

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Q: 7x sin 4 %3D nswer, including any

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

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

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Q: tan 0 If u= sec 0, then | de = sec 0 du (A Vūdu du © J, J "uvudu

A: We will solve the integration.

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

A: Here we have to prove that,

Q: Locate point E such that AE = DE = AB.

A: The Solution is given below-

Q: 3. If tan(a-iß) = x- iy , show that x? + y?-2ycoth2B = -1

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

A: We will evaluate the given integral.

Q: Assuming that sinu=20/29 and sinv=21/29 and that u and v are between 0 and π/2​,evaluate cos(u−v)…

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.