If p = sin2x + cos4x, then

(a) 3/4 ≤ p ≤ 1
(b) 3/16 ≤ p ≤ 1/4
(c) 1/4 ≤ p ≤ 1
(d) 1 ≤ p ≤ 2
Correct option: (a) 3/4 ≤ p ≤ 1
Given, p = sin2x + cos4x
= sin2x + (1 – sin2x)2
= sin4x + sin2x – 2sin2x + 1
= sin4x – sin2x + 1
= (sin2x – 1/2)2 + 3/4
p ≥ 3/4 p
= sin2x + cos4x
= sin2x + cos2x(1 – sin2x)
= (sin2x + cos2x) – sin2x cos2x
= 1 – sin2x cos2x
p ≤ 1
Therefore, 3/4 ≤ p ≤ 1

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