sin2x + cos4x = sin2x + (1-sin2x)2 = 1 - 3sin2xcos2x = 1 - 34sin22x
=> sin2x + cos4x = 1 - 34sin22x
so maxm value = 1
sin2x + cos4x = sin2x + (1-sin2x)2 = 1 - 3sin2xcos2x = 1 - 34sin22x
=> sin2x + cos4x = 1 - 34sin22x
so maxm value = 1
replace sin2x=1-cos2x
now consider the function
f(x)=x4-x2+1
it is an even function
so max value is when cos(x)=1or cos(x)=0 ...(from graph)
=1
the graph of the situation
see heres another easy method..
sin2x = sin2x.
cos4x ≤ cos2x.
adding,
sin2x + cos4x ≤ sin2x + cos2x.
≤ 1.
therefore max value =1.
isnt it a simple method???