The function f(x)=sin4x+cos4x increases, if

f(x)=sin4x+cos4x            =(sin2x+cos2x)2−2sin2xcos2x           =1−4sin2xcos2x2=1−sin22x2           =1−14(2sin22x)           =1−(1−cos4x4)=34+14cos4xHence, function f(x) is increasing when f'(x)>0f'(x)=−sin4x>0⇒sin4x<0Hence, π<4x<3π2  or  π4