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

1 Answer

May 31, 2018

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

Explanation:

#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) #

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