Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

Q: a) By expanding sin(2x+x) using double angle formulae, show that and sin 3x = 3 sin xr-4sin x.…

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Q: 41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For…

A: To show the following

Q: sec? a tan zdz Evaluate +C

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Q: 2.) Evaluate using wallis formula 1-x² dx and let x= sine

A: Given ∫01x41-x2dx By using 1-sin2(x)=cos2x And Wallis formula…

Q: 2 sin*x · cos³x dx

A: To evaluate ∫0π2 sin4x . cos3x dx using WALLIS formula.

Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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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: tan (w+2n eくな foo ttait

A: We have to find value of a and b :

Q: fhe coefpicient an fiderivative what? rin (2x ) in the fre of of F (A CoS is ン

A: We have to find the coefficient of sin 2x for given problem.

Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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Q: i) um asinx-sin2z ,u fünute, fünd the vaue the uimit. tana ofa and

A: Now, the limit is finite given so, the above must be 00form So,  a cos0-2cos0=0⇒a-2=0⇒a=2

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: Given f(x, y, z) = ze™" - a sin none of the choices 02-1/ 02²/ 0 01- ¹(), what is fax (0,2,1)?

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Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: Prove the following identities and show complete solution sin(u + v) + sin(u – v) = tan u cos(u + v)…

A: To prove the identity:sin(u+v)+sin(u-v)cos(u+v)+cos(u-v)=tanu Solution: We know:…

Q: 3. Prove that: tan-1z +z %3D

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Q: Prove the following statements: a) sinh (x+ y)= sinh x cosh y+ cosh xsinh y

A: (1) Prove sinhx+y=sinhxcoshy+coshxsinhy Concept used: sinhx=ex-e-x2 coshx=ex+e-x2 Proof: Take LHS…

Q: Evaluate using Wallis' Formula: So sin® x cos4 x dx -Tt/2

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Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

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

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Q: 2. Verify the following identities (a) sec e - tan@ =sec 0+tan6 sec 8+tan 6

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Q: prove the following identy (sect − sin(π/2 − t))(sec(π/2 − t)−sint) = tant − tantsin2 t

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Q: Q/prove that : (cos x) = -Sin X %3D

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Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: sin (z) 1-con(E)

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Q: Prove that: Sin'x+ cosx=I

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Q: If sinh x =tan t, 0<t<3/2 , then tanh x = sin t. Select one: O True O False

A: We have been given  sinh x= tan t for 0&lt;t&lt;3/2

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

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Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: tan? z sec? x + sec a Prove 1-cos I

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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: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: Prove the following identities. sin 3x v 3 sin x - 4 sin cSC X - 2 sin 3 sec x - 4 sin

A: Given query is to prove the identity.

Q: The value of a and b so that X(1 + a cos x)- b sin x lim =1 are .3 to 3 3 5 (b) 2 2 (a) 3 5 (c) 2 2…

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Q: Show that sin I dr

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Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: Use the Mean Value Theorem from §4.2 to prove that | sin(b) – sin(a)| < 16 – a| for any interval [a,…

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Q: Evaluate: sin z -dz +(°z – z)

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Q: xsinnx I= dx = 2 sinx

A: …

Q: a z given that z С. Show that sin-1У ôxôy ôyôx

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Q: х Given that t= tan , show that: 1-1? 2t d) sin x = 1+t? e) cosx = 1+1? 2t f) tanx = 1-?

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Q: 17) Prove the following: a) (sin x)(sec x)(cot x) 1

A: Since secx=1cosx  and cotx=cosxsinx Then LHS =  sinxsecxcotx=sinx1cosxcosxsinx

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: Given that sin x+y3=ax2y, express y' in terms of x and y.

A: Objective is to find y'.

Q: Sketch X,(t) and Xa(t) Where X,() = - Sim3t Sin3t %3D 3. X,(e) = /a Sin 3t %3D

A: To draw the graph of functions X1(t)=-13sin3t and X2(t)=13sin3t, substitute different values of t in…

Q: Prove the identity. cosh?x (cosh(2x) + 1) 2

A: