Question

cos4L+4cos2L+3=8cos^4L

Answer 1

u can write
\[\cos \ 2x = 2\cos^{2} x - 1\]
use this and expand ur expression until u get the answer

Answer 2

\(\bf cos^4(L)+4cos^2(L)+3=8cos^4(L)\quad ?\)

Answer 3

it;s
\[\cos( 4L) + 4\cos(2L) = 8\cos^{4}L\]

Answer 4

use...
\[\cos(2L) = 2\cos^{2}L -1\]
and
exapand
\[4 \cos (2L)...\]
it will be something like this
\[4 [ 2\cos^{2}L -1 ]\]

Answer 5

then...
take \[\cos (4L) \ as \ \cos(2\times2L)\]
then u can write..
\[\cos(4L) = \cos(2 \times2L) =2\cos^{2}2L - 1\]

Answer 6

so u can write...
\[\cos (4L) + 4\cos(2L) + 3\]
as
\[2\cos^{2}(2L) - 1 + 4[2\cos^{2}L - 1] + 3\]

Answer 7

now expand the
\[2\cos^{2} (2L) \]
using
\[\cos(2L) =2\cos^{2}L - 1\]
where u will get
\[2[ 2\cos^{2} L - 1]^{2}\]
now expand this expression..
\[2( 2\cos^{2}L - 1)^{2} = 2[4\cos^{4}L + 1- 4\cos^{2} L] = 8\cos^{4} L+ 2-8\cos^{2}L\]

Answer 8

now just write all the parts together... u will get ur answer..
\[8\cos^{4}L+2 -8\cos^{2}L -1 +4(2\cos^{2}L - 1) + 3\]

Answer 9

simplify this one( i mean remove brackets then add and subtract ...) u will get ur answer ...:)

got it :) ?