How do you use the power reducing formulas to rewrite the expression $cos^4x$ in terms of the first power of cosine?

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Answer 1 · 2018-05-31T19:12:57

$cos^4 x = 1/8 (3 + 4 cos 2x + cos 4x)$

$cos 2x = 2 cos^2 x - 1$

$cos ^2 x =1/2 ( 1 + cos 2x)$

$cos^2 2x = 1/2 ( 1 + cos 4x)$

$cos^4 x = (cos ^ 2 x)^2 = 1/4 (1 + 2 cos 2x + cos ^2 2x)$

$cos^4 x = 1/4 (1 + 2 cos 2x + 1/2( 1 + cos 4x) )$

$cos^4 x = 1/8 (3 + 4 cos 2x + cos 4x)$

How do you use the power reducing formulas to rewrite the expression cos^4xcos^4x in terms of the first power of cosine?