3. Prove that: tan-1z = Z 2 in () i-z.

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: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: b. Prove that 2cot (20) = cot(0) - tan(0)

A: To prove the identity.

Q: Prove that: 1. Z, Z2 =r¡r2[cos(0, + 02) + i sin(0, + 02)]

A: According to our company policy we can only answer first question and rest of questions can be…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: Prove that J5/2(x) = 2 TCX CScanned with CamScanner 3-x² 2 sin x - 3 COS X

A: Use the given information.

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: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

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A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: Prove that the inequality|cos(x)|≥1−sin2(x) holds true for allx∈R

A: Given inequality is

Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

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Q: Prove that J seccu) du - Ln/Sec (u)+ tan (w) + C

A: Integrated in general

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Prove that for all x € [1, 00), – sinh (- |cosh¯'(x)|) = Vx² – 1.

A:

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: Let In = fcos" rdx. Show that: 1 In n n-1 COS x sin x + n-1 -¹ n -In-2, n ≥ 2.

A:

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

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 0, + tan 02 + tan 03 + ......... + tan…

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Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: Prove that : 1 a) Sec'x= Cos!

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Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

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

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Q: Prove that the inequality | cos(z)| 21- sin"(z) holds true for all z € R

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Q: T/2 TT/6 sin x 2 1.)Prove that

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: Answer the following completely. Prove: cos x + sin x sin y = sin(32) cos (2) for all x and y such…

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Q: 2-If w(x, t) = Sin(x - + 3t) + Cos(2x+ 6t), prove that wtt = 9wxx %3D %3D

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Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: -Prove that: y" = 1 if y=csc(tan")

A:

Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

A: Given: ∫tan52xcos42xdx

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: A. Ifw= sin(x+bt)+cos(2x+ 2bt) . Prove that ôx? B. If f = x*y* + 2y sinx + x² lny then show that fxy…

A: A)

Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

A:

Q: Use the Second Fundamental Theorem of Calculus to evaluate 7. Part of the sin 2x the following…

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Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

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Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: Prove that : A) sin(h3x) =3sin(hx)+4sin(h³ n(n°x) B) 13 cos(hx) 3 C) 2tan(hx) tan(h2x) 1+ tan(h²x)

A:

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

A: Here we have to prove that,

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

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…