Home
Class 12
MATHS
If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| l...

If `|cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3)`, then

A

` x in [-(1)/(sqrt(3)), (1)/(sqrt(3))]`

B

` x in (-(1)/(sqrt(3)), (1)/(sqrt(3)))`

C

` x in [0, (1)/(sqrt(3))] `

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise LEVEL-2|58 Videos

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|15 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

  • JEE MAIN - 5

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|5 Videos

Similar Questions

Explore conceptually related problems

y = cos ^(-1)((1 - x^(2))/(1+ x^(2))) 0 lt x lt 1

If x lt 0 , the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x

If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

Solve sin^(-1) [sin((2x^(2) + 4)/(1 + x^(2)))] lt pi -3

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

Prove that : cos^(-1) x + cos^(-1) ((x)/(2) + (sqrt( 3-3x^2) )/( 2) ) = (pi)/ (3)

Differentiate cos^(-1)((1-x^2)/(1+x^2)) , 0lt xlt1 with respect to x

y = cos ^(-1)((2x)/(1 +x^(2))),-1 lt x lt1 . find dy/dx

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)