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



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ganeshie8
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start by factoring out cos^2 from first two terms

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

ganeshie8
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\(\huge 8(cos^4x cos^2x) + 1\)
is this the RHS ?

virtus
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yes

y2o2
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\[\large L.H.S = [ 8\cos^ 2(x)(\cos^2(x)  1) ]+1 = [ 8\cos^ 2(x)\sin^2(x) ]+1 \]
\[\large = [ 2 (2\sin(x)\cos(x))^2 ]+1 = [2(\sin(2x) ) ^2 ] + 1 \]
\[\large = 12\sin^2(2x) = \cos^2(2x)  \sin^2(2x) = \cos(4x) = R.H.S\]

ganeshie8
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good work @y2o2 :)

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

y2o2
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@ganeshie8 Thank you :)