1.20. Show that (a) r sin(ak) k=1 = r sin a r2-2r cos a+1'

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A: We need to integrate ∫11+sinxdx

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A:

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A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

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A:

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

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A: Since you have asked multiple questions in a single request we would be answering only the first…

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A:

Q: 3. Express the following function in terms of 'Sine & Cosine'; y (t) = 4 sin 2nt + 15 cos 2nt [

A: please see the next step for solution

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

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Q: 6. (a) 2 cos?t (b) 3 sin 2x

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Q: Differentiate. H(t) = cos2(t)

A: answer = -2sin2t   explanation is given in the below step

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Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

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Q: 1. Show that f(r) = sin(r + 3r) is equal to g(r) = -I Cos(I) at least once on -l. Hint: Think about…

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Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

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: 4.Evaluate y' for y = cos8x-1 sin8x and simplify the answer

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Q: en/6 .Evaluate: (i) cos" 30 sin 60 de Jo 2a (i) x(1- x*y/ dx (2ax-x) dx. (iii)

A: Note: Our guidelines we are supposed to answer only one question. Kindly repost rest question as the…