NTA Abhyas JEE Main2020MathematicsTrigonometric Ratios & IdentitiesPractice
If p = sin 2 x + cos 4 x , then
Options
- A3 4 ≤ p ≤ 1
- B3 16 ≤ p ≤ 1 4
- C1 4 ≤ p ≤ 1 2
- DNone of these
Correct answer
A. 3 4 ≤ p ≤ 1
Step-by-step solution
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