Question

sin4xcos4x=1-2sin2xcos2x

Answer 1

LHS- sin4x + cos4x

= (sin2x)2 + (cos2x)2

= (sin2x + cos2x)2 - 2sin2xcos2x  {since a2 +b2 = (a+b)2 - 2ab}

= 12 - 2sin2xcos2x {since sin2x +cos2x = 1}

= 1 - 2sin2xcos2x

= RHS

Hope it helps.

cheers!!!

Answer 2

hello mate
here is your solution

L.H.S.=sin4x+cos4x  
          =(sin2x)2+(cos2x)2     
       =(sin2+cos2x)2
−2sin2xcos2x   
         =(1)2−2sin2xcos2x      
      =1−2sin2xcos2x          
  =R.H.S.
⇒sin4x+cos4x=1
−2sin2xcos2x

I hope helps you