Prove the identity. cos(x + y) + cos(x – y) = 2 cos(x) cos(y)

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

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

Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

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Q: 7x Cos + COS cos 2.

A: According to trignometry formula:cos a +cos b =2cosa+b2 cosa-b2Given,cosx2+ cos7x2a=x2; b=7x2

Q: 7. The value of A. cosx - C O A O B О с O D dx √(1-x is B. sin '(x)+c C. cosx ' +2¢ D. cosx

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Q: (a) f(x) =cos (7æ) cos (Tx) 3

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Q: Determine ƒ such that (1, sin 1) is on the graph of f and e2z + 5e² + sin æ ifx 0

A: When derivative function is given, to find the actual function integrate the given derivative of the…

Q: If 0 < 0< and z= (sin 0+i(1- cos 0)) find in its simplest form arg z.

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Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

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Q: 36. (a) Prove the reduction formula 1 cos"-'x sin x + п S cos"x dx = | cos"-2x dx n n (b) Use part…

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Q: x sin (x²) cos(x²), from a = 0 to b = x 2

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Q: 2- Exercise: Evaluate a) L{4x2 – 3 cos(2x) +5e*} b) L{4+ sin (x) – e** } -

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Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

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Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: 1- co s x 1+co s x cos ae y = ln

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Q: The domain of the function f(x) = In(cos (x/3)) CO %3D

A: Given: f(x)=lncos−1x3

Q: Cos z Residue of cos. at z = 0 is %3D 1. 1 -1 3. 2 4. 0 2.

A: The residue of a function: f(z) at z=a is defined as Resz=af(z)=limz→az-af(z).

Q: If L{cos(ax)} then find L{x³ cos(ax)}. %3D p2+a²

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Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: f (0. 80108) = sin 3 (0. 80108) + cos 2 (0. 80108) – (0. 80108)²

A: Given,

Q: 2|C|k°]Re{el°• = k°{A cos(bln k)+B sin(b ln k)} 3 In k + B sin 2 [(4)-}. /3 In k 2 k1/2 { A cos

A: Equation 8.87 is a property   By using this property we can solve the equation Here  r  is a complex…

Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , ɛs = 0.002

A: Let f(x)=e-x(3.2sin(x)-0.5cos(x))…

Q: 1)1, e*, e2*, e3* 2) 1, e*, xe*,x²e* 3) 1, sin x , sin 2x 4) 1, sin x , cosx 5) 1, cosx, cos2x O A)…

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Q: 22. If y = (1- sin?x)i then y" is b. 1 COS X 2° а. C. - cos x d. -sin x sin x HIN HIN

A: The second derivative of the given function is solved in detail below.

Q: 3-26 · Evaluate the integral. 3. (x cos 5x dx

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Q: 1) Using the formula: cos(x +y) = cos x cos y - sin x sin y, prove in steps that: cos? x = %3D 1+cos…

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Q: 8. Solve: a sin() = { b 2 cos(a +) +1=0 on <a << 3 algebraically. on 0<a <10 using technology. %3D

A: 8.a) sinx5=23 on 0&lt;x&lt;10πb) 2cosx+π4+1=0 on π&lt;x&lt;3π

Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , Ɛs= 0.002

A: This is to be solved by successive bisection method.

Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

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Q: In cos (x - c1) + c2 y = In cos x +cj + c2

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Q: 2sin (2x) cos(2x) dx = cos (2x) + C sin (2x) + C 6. the above the above cos (2x) + C 6. sin (2x) + C…

A: We need to evaluate ∫2 sin5(2x) cos(2x) dx                           (1) Let sin(2x) = t On…

Q: X has a solution in Use the Intermediate Value Theorem to show that cos(x) (0, - 2

A: Using Intermediate Value Theorem to show that cos(x) =x is a solution in0,π2.

Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: 2. Show that: (i) sin (ii) A" cos (a + bx) = [2 sin bx + n cos - sin b (iii) A cot (a + br) = sin (a…

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Q: 1 cos Cos (n + 1)² n n=1

A: A telescoping series is any series where nearly every term cancels with a preceeding or following…

Q: Prove that : n/2 1 dx (a'sin'x + b’cos'x 4a°b³

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Q: Find y prime for y=(cos(x))^x

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Q: -11m. ii. cos-1(cos()) CO 6.

A: Given problem:- cos-1(cos(11π6))=?

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: b. cos(3n) + 2 sin(3n)

A: Solution :-

Q: 2tan x In (cos x) dx= A sin x [In(cos x)] + c cos x [In(cos x)] + C © -[In(cos x)]? +C D [In(sinx)]?…

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Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps that: cos? x = %3D…

A: Note - Since you have posted multiple questions, I am answering first one for you as per the…

Q: now that cos(ak – a/2) 2 sin(a/2) E sin(ak) : (1 %3D Taking the difference of cos(ak), A cos(ak) =…

A: We have to solve given problem:

Q: 12. Find all values of 0 in the interval [0, 2n) that satisfy the equation: cos 20 + cos 0 = 0

A: We need to find value of θ.