* (n + 1)(8² + 1)" 82n cos(n) In(6) 5. 8WI WI

Q: Find the sum from n=1 to infinity (sin(6/n)-sin(6/n+1))

A:

Q: 3 lim In cosy COS

A: Let,f(x)=limy→0y3lncosyput y=0,Therefore,=03lncos0=00 form,Therefore,using L-hospital…

Q: Maclaurin Series for cos 8x

A:

Q: b. Prove that 1+cos20 +isin2030 cos600 + isin600 1+cos20 -isin20

A:

Q: Find the area of the green shaded of the region where r = - cos(20) and r = - cos(8) as shown in…

A: Given: To find the area of the region here r= - cos 2θ   &     r= -cos θ.

Q: Suppose that f() Nin z on (0, ]. Find its Fourier sine and cosine series.

A: Given that f(x)=-16sinx The formula for fourier sine series is,…

Q: What would you substitute the integrand with in order to evaluate cos(29x) cos(31x) dx? (Do not…

A: The detailed solution is as follows below:

Q: 35 in n cos'n n Cos n du

A: Evaluate the ∫3sinx  cos3x dx

Q: 5) Integrate 2x cos (x²-5) with respect to x.

A:

Q: In 4 4. Co CoS X メ→0

A:

Q: Establish the identity 2 O A. cos2 0- sin ²0 1- cot² 0 О в. cos² 0-sin 20 1 - cot² 0 O C. cos ²0-sin…

A: We know, cot θ=cos θsin θ

Q: Find * sin (In æ) cos²(ln x) dx. cos (In x) , cos³ (In x) 3 cos (In x), cos³ (In x) 5 3 5 Option 3…

A:

Q: 14. Prove that (1- cos x) csc x = 1

A:

Q: Prove cos 4x = 8 cos4x − 8 cos2x + 1.

A:

Q: 4: Using appropriate Fourier series, Show that 4 -cos x=-sin 2x+sin 4x + 15 2 6. sin 6x+..... 35 4 3

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

Q: Can you show me a step-by-step proof

A: We need the following two identities to produce the required prove:

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

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: 1 1 Express in terms of csc(x) 1+ cos x 1- cos x

A: Given:     To determine: The given expression in terms of cscx

Q: sin(1-2n 1-2 sin(1+2a) 1-2 %3D

A:

Q: Use residue to evaluate the integral 3+ 2 cos 0 do 5 + 4 cos 0 0.

A: Given integral is, Let C denote the unit circle |z|=1. So,

Q: What is the cosine, sine and Fourier series of 1+cos^2(x) on [0, pi)?

A:

Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

A:

Q: sin(k/n). 1. cos(1) + 5/3. 2. cos(1) + 1/3. 3. cos(1) + 2/3 4. cos(1) – 1/3. O 1 O 2 O 4

A:

Q: 292 cos(25 x) cos(108 x) cos(4x) dx = x)) dx O 73 cos(-86 x) + cos(-78 x) + cos(128 x) + cos(136 O…

A:

Q: The Fourier series of the function f (x) = 2x² defined on [-7, n] is given by 272 + 3 00 Σ 8(-1)"…

A: To find the sum of the given series we use the Fourier series of given function and Parsevals…

Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: Evaluate cos O within AABC. 13 12 COS O Enter your next step here

A: We have given a right-angled triangle ∆ABC. We have to find the value of cosθ. The definition of the…

Q: Compute sin(sin( 3337 7 * ). -67 -57 7 -4T 7 -37 7 -27 O O O C

A: Computing the value

Q: prove tan^4x=cos4x-4cos2x+3/cos4x+4cos2x+3

A: Basic trigonometry proof

Q: Prove that cos120+cos840+cos1320+cos1560=(-1/2)

A:

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

A:

Q: apply Residue theorem to find the -2n cos20 do. 3+2sine

A: Use the following formulae, to obtain the solution. Let z=eiθ be a complex number. The real and…

Q: 4. Prove that tan x – cos x = sec x – cosʻ x - x- cos cos x – 1. :

A:

Q: Use residue to evaluate the integral 2л 3 + 2 cos 0 do 5 + 4 cos 0

A:

Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

A:

Q: 3) In (1+ Sin x)

A: Explanation of the answer is as follows

Q: 1-cos^3A/1-cosA = cos^2A + cosA+1

A: 1-cos3A1-cos A=cos2A+cos A+1

Q: sin 3rdx 8. Evaluate: S 4+cas²3x

A:

Q: /2 5 Evaluate the integral sin° xdx Please select file(s) Select file(s)

A: We have to find the integral

Q: Prove cos 4x = 8 cos4 x - 8 cos2 x +1.

A: In trigonometric ratio,cos2θ=2cos2θ-1

Q: cos( 2 tan1 (x/ 4)) = Select one: O 2x ( 16 - x2 )0.5 / ( 2x2 - 16 ) O 2x ( 16 - x2 )0.5/ ( 16 - 2x2…

A: Solution:-.

Q: Find the root (7 – 7i)/2 O +7/2[cos(x/4) – isin(x/4)] O +V98[cos(r/8) – isin(x/8)] O +7/2[cos(x/8) +…

A:

Q: If cos 30° + cos 60° + cos 90° + cos 120° + ... + cos 510° + cos 540° evaluate its sum.

A: Here we have to find the sum of the given cosine angle:…

Q: Prove that Cos45sin30/tan60csc45

A: