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Jan. 31, 2023•0 likes•2 views

Jan. 31, 2023•0 likes•2 views

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Powers of Cosine Express f(x) = cos 5x on 0 x pi as a linear combination of the functions K5 = {cosj x}j=0 rightarrow 5 . Solution cos5x = cosxcos4x - sinxsin4x = cosx(2cos 2 2x -1) - 2sinxsin2xcos2x =cosx(4cos 2 x -2 -1) - 4sin 2 xcosx(2cos 2 x - 1) =4cos 3 x - 3cosx - 4(2cos 3 x - cosx)(1-cos 2 x) =4cos 3 x - 3cosx - 4(2cos 3 x - 2cos 5 x - cosx + cos 3 x) =4cos 3 x - 3cosx - 8cos 3 x + 8cos 5 x + 4cosx - 4cos 3 x =8cos 5 x- 8cos 3 x + cosx plz rate me first, or i won\'t gt the credit... .

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- 1. Powers of Cosine Express f(x) = cos 5x on 0 x pi as a linear combination of the functions K5 = {cosj x}j=0 rightarrow 5 . Solution cos5x = cosxcos4x - sinxsin4x = cosx(2cos 2 2x -1) - 2sinxsin2xcos2x =cosx(4cos 2 x -2 -1) - 4sin 2 xcosx(2cos 2 x - 1) =4cos 3 x - 3cosx - 4(2cos 3 x - cosx)(1-cos 2 x) =4cos 3 x - 3cosx - 4(2cos 3 x - 2cos 5 x - cosx + cos 3 x) =4cos 3 x - 3cosx - 8cos 3 x + 8cos 5 x + 4cosx - 4cos 3 x =8cos 5 x- 8cos 3 x + cosx plz rate me first, or i won't gt the credit...