8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

Q: Derive formula (2) on page 601. cosucos v 5lcos (u – v) + cos (u + v)]

A: Given equation is cosucosv=12cosu-v+cosu+v. cosu-v=cosucosv+sinusinvcosu+v=cosucosv-sinusinv

Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

A:

Q: What is the exact value of 2sin(x/2) * cos(x/2) if sin of x = 3/5 and cos of x = 4/5 ?

A: To determine the exact value of the expression.

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(8), sin(0), 1) v = (sin(0),…

A: If u and v are orthogonal then u•v = 0  if u and v are parallel then u • v = | u | •| v |

Q: By using Cauchy laws find: sin (2) dz -i2 cos (2) dz 2-T3

A:

Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

A:

Q: Prove that 1.) 1+sec^2\theta \sin ^2\theta =\sec ^2\theta  2.) \frac{sin\theta }{1-cos\theta…

A: Please see the below picture for detailed solution.

Q: using De Moiuve's theor@m, show Tsat sin50 = 16 sino -20 sin o + 5 sin o ニ Hense salve z4 K -30%+ Ex…

A:

Q: tan(2x) = O cos(4x) – 1 sin(4x) COS O 1+ cos(4) sin(4x) O 1- cos(2) sin(2x) sin(4x) 1+ cos(4x)

A:

Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

A:

Q: 9 Determine fcot 20 sin' 20 d0.

A: 9. Given Integration can be simplified as

Q: Therefore, YZ-F Find the coc 1. (-2, 3, 5) an

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

Q: Find all solutions of 4sin^2xtanx−tanx= 0 that are in the interval [0,2π)

A: Given the equation  4sin2xtanx-tanx=0. We need to find the solution in the interval [0,2π)

Q: Prove that (7 sin2m-10 cos2n-10 = – B(m,n)

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 6) 1-cosx %3D 1+cosx (cotx - cscx)2

A:

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

Q: (b) в — р2'а, + psin'ф а, + 2pz sin' ф а, sin²o as + 2pz sin*ф а,

A: The complete solutions are given below

Q: If tan-0 = 1- a Prove that sec® + tam Ocosece = (2- a) 3. %3D %3D

A:

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: (45°) – tan (45°). Give the exact value of sec 2, 1 2/3-3

A: Use the trigonometric table to solve the given problem.

Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: sin(2³ + 42) f(2) = %3D 2² – 2z + 5

A: In this question, we find the radius of convergence for the given function. For the radius of…

Q: coS(T/11)-cos(2t/11)+cos(3t/11)-cos(4Tt/11)+cos(5rt/11)=?

A: To determine the value of the below expression. cosπ11−cos2π11+cos3π11−cos4π11+cos5π11

Q: Prove that X X sin 8 2 sin sin x 8 2,

A: The objective of the problem is to prove the equation. sin2π8+x2-sin2π8-x2=12sinx

Q: sin can be expanded to: sin 4 COS 2 cos - sin sin 2 O sin 4 sin -cos - + cos –sin 2 4 2 O sin + sin…

A: Given: sinπ4+π2 To find: expand the given trigonometric expression. The formula for…

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…

A:

Q: 4. Prove that equations are identities. l– cos4x a) tan 2x =, 1+ cos 4x

A: Given:

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5) (320° – sin 20 + jln5)*

A:

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

A:

Q: (7) (a) Prove the identity using Double Angle and Sum to Product Formulas: sin 10x cos 5x %3D sin 9x…

A:

Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: Use sin2 u + cos2 u = 1 to prove that 1 + cot2 u = csc2 u .

A: Since the equation is  1 + cot²u = csc²u

Q: Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13 %3D

A:

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

A:

Q: Compute sin (3r)dr (25z4+1)2 -

A:

Q: sin (tan' 8, zan-)= 0.35 O -0.35 O 0.40 O -0.40 O O O

A: Inverse Trigonometric ratios are just the opposite of Trigonometric ratios as Trigonometric ratios…

Q: By equating the real parts of cos5θ + j sin5θ = (cosθ + j sinθ)5 Show that cos5θ = 16cos5θ -…

A: Given By equating the real parts of cos5θ + j sin5θ = (cosθ + j sinθ)5

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(8), sin(0), 7) v = (sin(0),…

A:

Q: 14) Show that Cos e= 1- Sino COs o : |-Sinie

A: Given, cos2θ = 1-sin2θ We have to show that.

Q: how can 2sin(2β)cos(4β) be expressed as a sum?

A:

Q: compute:   ∫sin^3xcos^2xdx

A: We have to find:

Q: Prove CotA= sin2A/1-cos2A

A:

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A:

Q: Hint: the conjugate of the denominator #svon sinx - cosx + 1 sinx + 1 %3D xS200is sinx + cosx + 1…

A:

Q: 6. Show that in the interval (0, 7) 4 cos 2nx sinx = 元 Σ 4n2 -1

A:

Q: Xx sec( 2x

A: Solution:-