If p = sin 2 ⁡ x + cos 4 ⁡ x , then

Question

If p = sin 2 ⁡ x + cos 4 ⁡ x , then, 3 4 ≤ p ≤ 1, 3 16 ≤ p ≤ 1 4, 1 4 ≤ p ≤ 1 2, None of these

MARKS App · Accepted Answer

p = sin 2 ⁡ x + cos 2 ⁡ x ( 1 - sin 2 ⁡ x ) ⇒ p = ( sin 2 ⁡ x + cos 2 ⁡ x ) - sin 2 ⁡ x cos 2 ⁡ x ⇒ p = 1 − 1 4 ( 2 sin x cos x ) 2 ⇒ p = 1 − 1 4 sin 2 ( 2 x ) Max . value = 1 Min . value = 3 4

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