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Bingel [31]
3 years ago
12

How to express cos 3x in terms of cosx

Mathematics
1 answer:
Elena-2011 [213]3 years ago
5 0
\cos3x=\cos(x+2x)=\cos x\cos2x-\sin x\sin2x
=\cos x(\cos^2x-\sin^2x)-2\sin^2x\cos x
=\cos^3x-\cos x\sin^2x-2\sin^2x\cos x
=\cos^3x-3\cos x\sin^2x
=\cos^3x-3\cos x(1-\cos^2x)
=\cos^3x+3\cos^3x-3\cos x
=4\cos^3x-3\cos x
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