1 - 2cos²( π/4 -4x) = 2 [1/2 - cos² ( π/4 -4x] =
factor fortat 2
stim cos π/4= √2 /2 atunci cos² π/4= 1/2
= 2 [ cos² π/4 - cos²( π/4 - 4x )] = 2 [ cos π/4 + cos ( π/4 -4x)] ·[ cosπ/4 - cos ( π/4 -4x) ] = transformam parantezele in produs
= 2 ·2 cos [ ( π/4 + π/4 -4x) /2 ] ·[ cos ( π/4 - π/4 +4x)/2]· (-2) [ sin( π/4 +π/4 -4x) /2 ] ·[ sin( π/4 -π/4 +4x) /2 ]=
=8 cos( π/4 -2x) ·cos 2x ·sin(π/4-2x) ·sin2x=formam dublul unghi
2sint ·cost = sin2t
= 2 sin[ 2 ( π/4 -2x )] · sin[2 (2x)] sin( π/2 -4x ) = cos4x
= 2 sin4x· cos 4x = sin8x
