Question

verify identity: cos 4u= 8cos^4 u - 8cos^2 u + 1

Answer 1

remember- >\[\cos(2u)=\cos^2u-\sin^2u=2\cos^2u-1\]
start from the big one the right side
\[
8\cos^4u-8\cos^2u+1=4(2\cos^2u)^2-4(2\cos^2u)+1\\
=2[\cos(2u)+1]^2-4[\cos(2u)+1]+1\\
=2[\cos^2(2u)+2\cos(2u)+1]-4\cos(2u)-4+1\\
=[2\cos^2(2u)]+4\cos(2u)+2-4\cos(2u)-3\\
=[\cos(4u)+1]-1\\
=\cos(4u)
\]

Answer 2

thanksss !