How do you use the power reducing formulas to rewrite the expression #cos^4x# in terms of the first power of cosine? Trigonometry Trigonometric Identities and Equations Double Angle Identities 1 Answer Dean R. 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) # Answer link Related questions What are Double Angle Identities? How do you use a double angle identity to find the exact value of each expression? How do you use a double-angle identity to find the exact value of sin 120°? How do you use double angle identities to solve equations? How do you find all solutions for #sin 2x = cos x# for the interval #[0,2pi]#? How do you find all solutions for #4sinthetacostheta=sqrt(3)# for the interval #[0,2pi]#? How do you simplify #cosx(2sinx + cosx)-sin^2x#? If #tan x = 0.3#, then how do you find tan 2x? If #sin x= 5/3#, what is the sin 2x equal to? How do you prove #cos2A = 2cos^2 A - 1#? See all questions in Double Angle Identities Impact of this question 65353 views around the world You can reuse this answer Creative Commons License