Question

Show that cos(4)x =8(cos^(4)x -cos^(2)x)+1

Answer 1

start by factoring out cos^2 from first two terms

Answer 2

8cos^2(cos^2x -cosx)+1

Answer 3

\(\huge 8(cos^4x -cos^2x) + 1\)

is this the RHS ?

Answer 4

yes

Answer 5

\[\large L.H.S = [ 8\cos^ 2(x)(\cos^2(x) - 1) ]+1 = [ -8\cos^ 2(x)\sin^2(x) ]+1 \]

\[\large = [ -2 (2\sin(x)\cos(x))^2 ]+1 = [-2(\sin(2x) ) ^2 ] + 1 \]
\[\large = 1-2\sin^2(2x) = \cos^2(2x) - \sin^2(2x) = \cos(4x) = R.H.S\]

Answer 6

good work @y2o2 :)

Answer 7

thanks guys, i will look at this later because i am super sleepy

Answer 8

@ganeshie8 Thank you :)