How can I rewrite 8 cos 4x in terms of cos x? If you could give a detailed explanation, that would be great!

1 Answer
Nov 17, 2017

8cos4x=64cos^4x-64cos^2x+8.8cos4x=64cos4x64cos2x+8.

Explanation:

Recall that, cos2x=2cos^2x-1.cos2x=2cos2x1.

:. cos4x=2cos^2 2x-1,

=2(cos2x)^2-1,

=2(2cos^2x-1)^2-1,

=2(4cos^4x-4cos^2x+1)-1,

:. cos4x=8cos^4x-8cos^2x+1.

rArr 8cos4x=64cos^4x-64cos^2x+8.