Sin6x cos 6x 3sin2x cos2x
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= cos u dy _ dydu By the Chain Rule, du dr = cosu X 4 = 4cosu = 4cos4x In practice, we generally do not use the substitution method to apply the Chain Rule. dy — = cos6x. — (6x) = cos 6x.6 = 6 cos6x If y = sin6x Here are two more examples of the use of the Chain Rule: (i) If y = sinx2 dy = cosx2.(2x) = 2.r cos2x (ii) If y = cos(3x2 + x) dy
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sin8x.cos cos8x.sin sin6x.cos cos6x.sin 3 3 6 6 S S S S sin 8x sin 6x 36 ... 2sin x 3sin2x 32 1 cos2x 3sin2x 3 3sin2x cos2x 2 31 sin2x cos2x 1 22 sin2x.cos cos2x.sin 1 66 SS sin 2x 1 6
[PDF File]Integration of cos x cos2x cos3x
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Integration of cos x cos2x cos3x Last updated at March 11, 2021 by Teachoo Transcript Ex 5.5, 1 Differentiate the functions in, cos . cos2 . cos3 Let y = cos . cos2 . cos3 Taking log both sides log = log (cos .cos2 .cos3 ) log = log (cos ) + log (2 ) + log (cos3 ) Differentiating both sides . . . .
[PDF File]Exo7 - Exercices de mathématiques
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3.En déduire un polynôme de degré 2 dont les racines sont a et b puis les valeurs exactes de cos 2p 5 et sin 2p 5. Correction H [005075] Exercice 14 **I Calculer une primitive de chacune des fonctions suivantes : 1. x 7!cos2 x, 2. x 7!cos4 x, 3. x 7!sin4 x, 4. x 7!cos 2xsin x, 5. x 7!sin6 x, 6. x 7!cosxsin6 x, 7. x 7!cos5 xsin2 x, 8. x 7 ...
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B) 4COS4 —+ cosx+l— —0; —=cosx+3. A) 4cos 2.2.4. a) tg2x+3= cos4 x B) 2 tg4x— cos4 x cos4 x r) 8sin = cosx ; 6) ctg4x+23= sin 4 x r) 7+ 3ctg2x=
[PDF File]Formulaire de trigonométrie circulaire
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cos(2x) = cos 2(x)−sin (x) sin(2x) = 2sin(x)cos(x) = 2cos2(x)−1 = 1−2sin2(x) tan(2x) = 2tan(x) 1−tan2(x) Formules du demi-angle cos 2(x) = 1+cos(2x) 2 sin (x) = 1−cos(2x) 2 tan(x) = sin(2x) 1+cos(2x) = 1−cos(2x) sin(2x) En posant t = tan x 2 pour x 6≡π [2π], on a : cos(x) = 1−t2 1+t 2, sin(x) = 2t 1+t et tan(x) = 2t 1−t ...
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= cos 6x ˇ 4 ; ä) cos x+ cos ... cos2x p 3sin2x= p 3; á) p 2cos x 2 p 2sin x 2 = 1; â) 5sinx+ 12cosx= 13. 12. Ðåøèòå óðàâíåíèÿ: à) sin4x sin6x= 0; å) sin2 2x+ sin2 4x= 1; á) cos 3x+
[PDF File]PHƯƠNG TRÌNH BẬC NHẤT VỚI SINX VÀ COSX
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8x 6x k2 x 3 6 12 7 8). sinx cosx 2 2sinx.cosx (1) 1 sinx cosx 2sin2x 1 1 sinx cosx sin2x 2 2 sinx.cos cosx.sin sin2x 4 4 2x x k2 x k2 4 4 sin x sin2x , k 4 k2 2x x k2 x 4 4 3 Vậy nghiệm của phương trình: k2 x k2 ,x , k 4 4 3 9).2sin x 3sin2x 32 1 cos2x 3sin2x 3 3sin2x cos2x 2 3 1
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2 e 2 e cos 2x. n 1 2x 2 2x. n 4. − =+ + − π Example 3 : Find n. th. derivative of sin. 3. x cos. 3. x. Solution : 3 . y = sin x cos. 3. x 3 3= 1 8 (8 sin x cos x) 3 = 1 8 (2 sin x cos x) 3 = 1 8 (sin 2x) 3 y = 1 8. sin 2x . 3 3 3 3. sin3A 3sinA 4sin A 4sin A 3sinA sin3A 13 1 y sin2x sin6x 4sin 2x 3sin2x sin6x 84 4 31 sin 2x sin2x sin6x 44 ...
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3 13. my; ixlS¾K i(a) xLHd j,udmdxlh yd úia;drh fidhkak. (i) cos – i sin (ii) 1 + cos + i sin (iii) 1 – cos + i sin (iv) 4 cos /6 + 2 i sin /6 (b) z 1, z 2 ixl¾K ixLHd folla úg z 1 z 2 ixlS¾K iLHdjg wkqrEm ,ËHh wd.kaâ igykl ks¾udKh lrk wdldrh fmkajkak. z ixlS¾K ixLHdjla wd.kaâ igykl P ,ËHhlska ksrEmKh fõ kï, z2 ixl¾K ixLHdj ksrEmKh lrk ,ËHh wd.kaâ igyfka
[PDF File]The double angle formulae
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The formula cos2A = cos2 A −sin2 A 3 4. Finding sin3x in terms of sinx 3 5. Using the formulae to solve an equation 4 www.mathcentre.ac.uk 1 c mathcentre 2009. 1. Introduction ... Suppose we wish to solve the equation cos2x = sinx, for values of x in the interval −π ≤ x < π.
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cos 3x cos2x =8cos2x Bài 1.17. Chứng minh sin 6xcos2x+sin2xcos x = 1 8 (1 cos42x) Bài 1.18. Chứng minh sin 4x+cos x 1 sin6x+cos6x = 2 3: Bài 1.19. Chứng minh các đẳng thức sau 1. 3 4cos2a+cos4a 3+4cos2a+cos4a =tan4a 2. sin22a+4sin2a 4 1 28sin2a cos4a = 1 2 cot4a 3. cota tana 2tan2a 4tan4a =8cot8a 4. tan(x p 2)cos(3p 2 +x) sin3(7p ...
[PDF File]Преобразования тригонометрических уравнений
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2sin7xcosx 2sin5xcos3x= 0 , sin8x+sin6x (sin8x+sin2x) = 0 ,, sin6x sin2x= 0 , sin2xcos4x= 0: Если sin2x = 0, то x = ˇn 2 (n 2Z). При этих значениях xимеем cos2x = 1, так что неравенство(3)выполнено. Пустьтеперьcos4x= 0,тоесть 0 = cos 22x sin 2x= (cos2x sin2x)(cos2x+sin2x):
[PDF File]Chapter 7
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= cosxand cos x 2 = sinx. You may make the substitution at the beginning and then antidi erentiate, or rst antidi erenti-ate and then substitute. 14. See previous question. 15. Z cos 2x+ 2ˇ 3 dx = 1 2 Z 2cos 2x+ 2ˇ 3 dx = sin 2x+ 2ˇ 3 + c 16. Z sin( x)dx= Z sinxdx = cosx+ c 17. Z 4 cos2 x dx= 4tanx+ c 18. Z 1 cos2 4x dx= 1 4 Z 4 cos2 4x dx ...
[PDF File]Class Notes
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sin6x cos2x dx — sin6x cos6x dx cos2x sin6x — cos6x sin6x dx cos(2x) — cos(6x) sin6x dx . 3. sinx cos2x sin3x dx cosmx cosnx dx 1. sinmx cosnx dx cos8x 32 cos4x 16 cos12 48 —cos8x 16 cos4x —cos12x 24 Putting the value of Il and 12 from (2) and (3) to (1), we get
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