The correct option is B False
cot3x1+cot2x
=tan2(x).cot3x1+tan2(x)
=cot(x)1+tan2(x)
Hence the above expression becomes,
tan2x+cotx1+tan2(x)
=tan3x+1(tanx)(tan2x+1)
=cos3(x)(sin3x+cos3x)cos3x.sinx
=cos3x+sin3xsinx
RHS
=1−2sin2xcos2xsinx.cosx
=(sin2x+cos2x)2−2sin2xcos2xsinx.cosx
=sin4x+cos4xsinx.cosx
Hence LHS≠RHS