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The equation cos4x = 1+8cos^4-8cos^2 can be solved by re-writing as 2(cos2x)^2 -1 and factoring out which yields the correct answer, however based on what i've seen in other double angle identity equations one can re-write cos4x as cos(2x + 2x).

I believe this can be written as [(2cos^2 - 1)(2cos^2-1)] + [(2cos^2-1)(2cos^2-1)], however the answer then comes out to 8cos^4-8cos^2+2. So it's off by "+1".

What about my thinking is flawed? They can't both be correct!

Thanks for your help.

Joe