Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsTrigonometric Ratios & IdentitiesPractice

If p = sin 2 ⁡ x + cos 4 ⁡ x , then

Options

  1. A3 4 ≤ p ≤ 1
  2. B3 16 ≤ p ≤ 1 4
  3. C1 4 ≤ p ≤ 1 2
  4. 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

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

Let = (1 - 2 ( 11 ) ) (1 - 2 ( 3 11 ) ) (1 - 2 ( 9 11 ) ) (1 - 2 ( 27 11 ) ) (1 - 2 ( 81 11 ) ) . Then the value of 5 - ^2 is _____________. 2026If A = 3^ 9^ + 9^ 27^ + 27^ 81^ and B = 81^ - 3^ , then B A is equal to _____. 2026Let P = [0, 4 ] : ^2 1 and S = a Z : 2( ^8 - ^8 ) 2 = a^2, P . Then n(S) is: 2026If ( 18 ) ( 5 18 ) ( 7 18 ) = K , then the value of ( 10K 3 ) is : 2026If ( A - B ) A + ² C ² ~A =1, ~A , ~B , C (0, 2 ) , then 2026If x= 5 12 for some x ( , 3 2 ) , then 7 x ( 13 x 2 + 13 x 2 )+ 7 x ( 13 x 2 - 13 x 2 ) is equal to 2026The value of 3 cosec 20^ - 20^ 20^ 40^ 60^ 80^ is equal to 2026The least value of ( ² -6 +3 ² +2 ) is 2026 Full Trigonometric Ratios & Identities list All NTA Abhyas JEE Main PYQs