EAMCET QUE...

max value occurs at x = 90/0 degrees
max A = 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???