Trigonometry

If A = sin2 x + cos4 x, then for all real x

  1. 3/4 ≤ A ≤ 1
  2. 1 ≤ A ≤ 2
  3. 3/4 ≤ A ≤ 13/16
  4. 13/16 ≤ A ≤ 1

Answer

A = sin2 x + cos4 x

= sin2 x + (1 - sin2 x)2

= sin4 x - sin2 x +1

= (sin2 x - 1/2)2 + 3/4

The correct option is A.