Answered

Find an identity for cos(4t)

cos

⁡

(

4

t

)

in terms of cos(t)

cos

⁡

(

t

)

.

Verified Answer :

arthurpdc

We must know that \(\cos(2x)=2\cos^2(x)-1\). So:

\(\cos(4t)=\cos(2\cdot2t)\\\\ \cos(4t)=2\cos^2(2t)-1\\\\ \cos(4t)=2(2\cos^2(t)-1)^2-1\\\\ \cos(4t)=2(4\cos^4(t)-4\cos^2(t)+1)-1\\\\ \cos(4t)=8\cos^4(t)-8\cos^2(t)+2-1\\\\ \boxed{\cos(4t)=8\cos^4(t)-8\cos^2(t)+1}\)

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