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

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Answer 1 · 2017-11-17T17:31:55

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

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

#:. 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.#