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vredina [299]
3 years ago
7

Find an identity for cos(4t)

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
5 0
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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