cos 3x formula

cos 3x formula Answer link cos 3x 4 cos 3 x 3 cos x I have no idea what the product rule is or how it applies There are a few different ways to get the triple angle formula for cosine For example it follows from De Moivre cos 3x i sin 3x cos x i sin x 3 cos 3 x 3 i cos 2 x sin x 3 i 2 cos x sin 2 x i 3 sin 3 x cos 2 x 3 cos

The answer is 1 2 sinx cosx 2 sin 2x We apply a 3 b 3 a b a 2 ab b 2 Here a sinx and b cosx So sin 3x cos 3x sinx cosx sin 2x sinxcosx cos 2x But sin 2x The answers are cos3x 4cos 3x 3cosx and sin3x 3sinx 4sin 3x We need cos 2x sin 2x 1 According to Demoivre s theorem cosx isinx n cosnx isinnx Here n 3 So cos3x isin3x cosx isinx 3 cos 3x 3icos 2xsinx 3i 2cosxsin 2x i 3sin 3x cos 3x 3icos 2xsinx 3cosxsin 2x isin 3x cos 3x 3cosxsin 2x i 3cos 2xsinx sin 3x

cos 3x formula

cos 3x formula
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Trigonometric Function Derivation Of Formula For Triple Angle Cos3x
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Integral Of Cos 3x substitution YouTube
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Prove the trig identity cos 3a 4cos 3 x 3cos x Apply the trig identity cos a b cos a cos b sin a sin b cos 3x cos 2x x cos 2x cos x sin 2x sin x Use the trig identities cos 2x 2cos 2 x 1 sin 2x 2sin x cos x cos 3x 2cos 2 x 1 cos x A different way use reduction formula cosnxdx n 1 n cosn 2xdx cosn 1x sinx n use n 3 cos3xdx 3 1 3 cos3 2x cos3 1x sinx 3 cos3xdx 2 3 cosxdx cos2x sinx 3 cos2x 1 sin2x cos3xdx 2 3 sinx 1 sin2x sinx

If we apply this rule to the given example we get sin3xos3x sin6x 2 Answer link This can be simplified as sin6x 2 According to the double angle formula sin2x 2sinxcosx From this we can say that sinxcosx sin2x 2 or more generally sinnxcosnx sin2nx 2 If we apply this rule to the given example we get sin3xos3x sin6x 2 Prove cos 3x 4cos 3 x 3cos x Apply the trig identities cos a b cos a cos b sin a sin b

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Penjabaran Cos 3x De Eka
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Answer link See below It s a little tricky but try setting the equation 0 cos 3x cosx cos 3x cosx 0 Now factor out cosx cosx cos 2x 1 0 And now factor the difference of two squares cosx cosx 1 cosx 1 0 Set each factor equal to 0 and solve using your unit circle 1 cosx 0 x pi 2 3pi 2 2 cosx 1 0 cosx 1 x pi 3 cosx 1 0 cosx 1 Solution Use trig identity to transform cos x cos 3x F x 2cos 2x cos x cos 2x cos 2x 2cos x 1 0 Next solve the 2 basic trig equations 2 Transform a trig equation F x that has many trig functions as variable into a equation that has only one variable The common variables to be chosen are cos x sin x tan x and tan x 2

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How Do You Integrate Int Cos 3x Dx Socratic
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Example 7 ii Find Integral Sin 2x Cos 3x Dx Teachoo
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cos 3x formula - [desc-12]