Home
Class 12
MATHS
If A = sin^2x + cos^4 x, then for all re...

If `A = sin^2x + cos^4 x`, then for all real x :

A

`(3)/(4) le A le (13)/(16)`

B

`(3)/(4) le A le 1`

C

`(13)/(16) le A le 1`

D

`1 le A le 2`

Text Solution

Verified by Experts

The correct Answer is:
B
`A = sin ^(2) x + cos ^(4) x `
`= 1- cos ^(2) x + cos ^(4)x`
`= 1 - cos ^(2) x (1- cos ^(2)x)`
` = 1- cos^(2)x sin ^(2) x `
` = 1- ( sin ^(2) 2x)/( 4)`
Now, `0 le sin ^(2) 2 x le 1`
`rArr - (1)/(4) le - ( sin^(2) 2x )/(4) le 0`
`rArr (3)/(4) le 1 - ( sin ^(2)2x)/(4x) le 1 `
`rArr 3//4 le A le 1`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise JEE Advanced Previous Year|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Numerical)|38 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If A= sin^(2) x + cos^(4) x then for all real x

If A = "sin"^(2)x + cos^(4)x then for all realx :

If A=sin^(2)x+cos^(4)x, then for all real x:

If A=sin^(2)x+cos^(4)x, then for all real x: (1) (3)/(4)<=A<=1(2)(13)/(16)<=A<=1(3)1<=A<=2(4)(3)/(4)<=A<=(13)/(16)

Let y=sin^(2)x+cos^(4)x . Then, for all real x (a) the maximum value of y is 2 (b) the minimum value of y is 3/4

A function f (x) which satisfies, f ' (sin ^(2)x) = cos ^(2) x for all real x & f (1)=1 is

If A = sin^(2)x + cos^(4)x , where x in a real number

If a=(1)/(5cos x+12sin x) then for all real x