7. Evaluate sin xcos x dx. cos* x +C 4 1 C) 4 sin* x A) +C 1 sin* x B) 4 cos* x +C D) +C 4 a O c O d

Q: Prove that n r=0 "C, sin rx.cos (n-r)x=2"-¹x sin nx. 1

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

A:

Q: If sin 0 + sin²O = 1, then cos40 + cos³0 + 2cosg = %3D %3D A) O B) -1 C) 1

A: To find: The value of cos4θ+cos8θ+2cos6θ. Given: The equation is sin θ+sin2θ=1. Formula used: The…

Q: 11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx'…

A: 11.Given,∫x.In x dx

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A:

Q: sin(tan-1))

A: SOLUTION-

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A: V=∫3sinx+5secxtanxcosxdxtanx=sinxcosxsecx=1cosx∫1xdx=lnx

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A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: 13) 3 sin x +5 sec x tan x cos x dx

A:

Q: 18) sin 3 dt t

A:

Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: DI Ify x Sin x, x'sin x, .2 O a) 2 sin +x cos x O b) 2x sin x + x I SOƆ cos x O) 2x sinx - x cos x…

A: Use product rule of differentiation. D(uv) = D(u).v + u.D(v)

Q: 12 12) Find cos 0 if csc 0 11 11) Find sin 0 if csc 0 = 3 A) 5 В) 12 V23 A) V23 B) 12 23 11 C) 12 4…

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Q: Evaluate ſe* 2x cos 2x dx cos 2x a) 2esin 2x + C b) -+c 2 c) ecos2x +c sin 2x e d) – +c

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Q: 9. Evaluate sin x dx a) S, 1+sin x b) S sec x tan x- csc²x *dx secx + cotx

A:

Q: appropriate formula for 9. What is the f sin7 x cos x dx ? A) sin x cos x dx | cscx cosx dx B) C)…

A: We have to find solution of given indefinite integral.

Q: be +50 + 10 cos z)dr= %3D

A:

Q: 15. If S Sin 0 and C = Cos 0, simplify: S.C i) √√1-S² S.√√1-S2 ii) C.√1-C² C S iii) + S C (ans..:i)…

A: If , , simplify:i) ,ii) ,iii)

Q: Evaluate the following commutators:

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: (5е? + 9* — 8 sin x)dx - 8 sin æ) de O 5e* + x° – 8 cosx + c x° - 8 cos x + c О Бе + x —— 8 sin x +…

A: Solving the problem by doing the integration.

Q: 2) f(3x + cos(x))[3x +2sin(x)-31dx = A) 3x+2sin(x)- 3+C B)13x+ 2sin(x)- 31 +C C) other

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Q: If f(x) = cos (x) + 3x + 2, x e [0, 1], then f-(5) 3= %3D A) cos + 17. B) 5m cos +17 C) 0. D) 2. E)…

A:

Q: Sæ³ cos(x*) dæ =

A: We solve it by u part method , ∫x3cosx4dx Let u = x4 Differentiate both side , we get   du = 4x3dx…

Q: 9-simplify sin 3π/4 сos π/3 +cos 3π/3 sin π/3 a) Sin 13π/12 b) Sin 5π/12 c) Cos 13/12 d) Cos 5π/12

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Q: Prove ONE of the follow sin x+ cos 2x-1 tan x %3D a) cos x-sin 2x

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Q: 11. Prove each identity. T cos 2x + 1 a) cot x %3D sin 2x sin 2x b) 1 - cos 2x cot x c) (sin x + cos…

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Q: Find L{10) } s(s²+16) 1+cos(4t) 16 1-cos(4t) 4. 1-cos(4t) 16 1+sin(4t) 4 1-sin(4t) 16

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Q: Show that n. In(cos 2k+2) = - In (2"+ sin 2n+2). k=0 Hint: sin 20 = 2 sin 0 cos 0.

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Q: : [5 cos(5)r – 3 csc²(x) ] dz =. Evaluate: O sin(5z) + 3 cot(x)+C O sin(5z) + 3 tan(x) + C O -…

A:

Q: Step by step

A: We will need integration by parts for this problem. So we assume u and dv then find du and v

Q: 9) cos A 11) sin Z 13) cos X 24 15 17 15) tan X 8 X 24 Y 10) cos Z 15 Z 12) sin C B 25 36 A 27 18 45…

A: Step 1:Step 2: Step 3: Step 4:

Q: 7) (*x* cos xdx frese" – nde 8) xcsc 4

A:

Q: sin + 4 4 can be expanded to: sin sin 4 4 cos cos 4 o sin - cos 4 sin 4 sin 4 o cos -sin 4 + cos 4…

A: Solve the following

Q: Ys l.2 Sin(o+꽃)

A: r=1-2sin2(θ+π3)