kaossoccer17 kaossoccer17

09-12-2016
Mathematics

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Find an identity for cos(4t) in terms of cos(t)
cos(4t)=

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wizard123 wizard123

09-12-2016

Use double angle formula for cosine:
[tex]cos (2a) = 2cos^2(a) - 1[/tex]

Apply to cos(4t)
[tex]cos (2(2t)) = 2 cos^2 (2t) - 1 \\ cos (2t) = 2 cos^2 t - 1[/tex]
Sub 2nd equation into 1st equation:
[tex]cos(4t) = 2 (2 cos^2 t -1)^2 - 1 \\ = 8 cos^4 t -8cos^2 t +1[/tex]

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