Let #A = Cos( pi/5 )*Cos( 2*pi/5 ) #
But #Sin( 2*X ) = 2Sin( X )*Cos( X ) #
#=> Cos( X ) = Sin( 2*X ) / [ 2*Sin( X ) ] ------ > (1 ) #
When# X = Pi / 5# Then
#Cos( Pi/5 ) = Sin( 2*pi/5 ) / [ 2*Sin( Pi/5 ) ] #
And# A = Cos( pi/5 )*Cos( 2*pi/5 ) #
#= [ Sin( 2*Pi/5 ) * Cos( 2*Pi/5 ) ] / [ 2*Sin(Pi/5) ] #
Following Equation ------ > ( 1 ) Then
#Sin(2*Pi/5) * Cos(2*Pi/5) = [ Sin ( 4*Pi/5 ) ] / 2 #Then
And #A = Cos( pi/5 )*Cos( 2*pi/5 ) #
#= [ Sin( 2*Pi/5 ) * Cos( 2*Pi/5 ) ] / [ 2*Sin(Pi/5) ] #
#= [ Sin ( 4*Pi/5 ) ] / [ 2 * 2 * Sin( Pi/5 ) ] #
But# Sin ( 4*Pi/5 ) = Sin ( Pi - Pi/5 ) #
#= Sin ( Pi )*Cos( Pi/5 ) - Cos( Pi )*Sin( Pi/5 ) = Sin ( Pi/5 ) #
Then #A = [ Sin ( 4*Pi/5 ) ] / [ 2 * 2 * Sin( Pi/5 ) ] #
#= [ Sin (Pi/5 ) ] / [ 2 *2 *Sin (Pi/5 ) ] = 1/4 #
