-1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

Q: 1 + sin 4x cos 4x + C 8. 13.

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Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

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Q: 2. Identify each of the following polar equations and state the correct graph: a. r 2-2 cos 0 i. ii.…

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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: Evaluate cos(9x)cos(3x)dæ.

A: Given definite integral ∫0πcos(9x)cos(3x)dx compute the difinite integral It is in the form of…

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: True or false: If cos A is negative, then cos (A/2) is negative as well.

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Q: Evaluate cos³ (72) sin(7x)dr / COS³ + C

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Q: 1 + cos 20 57. Show that cos?e = 2

A: Show that the given identity, cos2θ=1+cos2θ2. Addition property:  cosA+B=cosAcosB-sinAsinB

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: Determine the exact value of cos T + TT 3 6

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Q: Plot each complex number: 1. -3i 3 2. 1. -2 -1 5. -11 -2

A: In complex plane  z = x + iy    = (x,y)

Q: 6T cos 8 de : so O o o O

A: Here we will solve the  given integral,

Q: E. Inverse D- Ope rator 1. (D* + 3D + 2)y• 24cosOK + 3D + 2) y- 24 cos3x

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Q: Sec A - cos A is identically equal to

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Q: L{cos 5t} OS

A: To find the laplace transform of cos2 5t. We use the cosine formulas to solve the given question. We…

Q: verify the identity seco+1 2 COS 2 - 2 sec 0

A: Verify the identity: cos2θ2=secθ+12secθ

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

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Q: Go to your book on Section 5.2 problem set page 309 problem number 44. Find the exact answer for cos…

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Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

Q: 1 8. Let the integral I = = [ f(x) dx = 0 So COS (72) dx be evaluated using the Monte-Carlo method.…

A: (a) To find the variance of the crude Monte Carlo estimator \( X = f(U) \), where \( U \sim…

Q: Evaluate COs 2 4 – x² dx

A: use the property of even function and odd function to evaluate the integral.

Q: cos3θ+cos4θ=0.

A: Consider the given equation, cos3θ+cos4θ=0 By using the formula, cos(a + b) + cos(a - b) =…

Q: x + 2 cos x 20. у -

A: If y = u/v, y' = (v*u' - u*v')/v^2.  d(cos x)/dx = -sinx d(x+2) = d(x) + d(2) = 1.