Question #f6f93

1 Answer
Apr 18, 2016

Proof below

Explanation:

8sin^2xcos^2x=2*2sinxcosx*2sinxcosx8sin2xcos2x=22sinxcosx2sinxcosx
First rule you'll need to know: 2sinAcosA=sin2A2sinAcosA=sin2A
=2*sin2x*sin2x=2sin2xsin2x
=2*sin^2(2x)=2sin2(2x)
=1-1+2*sin^2(2x)=11+2sin2(2x)
=1-(1-2sin^2(2x))=1(12sin2(2x))
Second rule you'll need to know: 1-2sin^2A=cos2A12sin2A=cos2A
=1-cos4x=1cos4x