Home
Class 12
MATHS
If cos (2 sin^(-1) x) = (1)/(9), then fi...

If `cos (2 sin^(-1) x) = (1)/(9)`, then find the value of x

A

`pm 1`

B

`0`

C

`pm 1/3`

D

`pm 2/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `sin^(-1) x = theta`. Then,
`cos 2 theta = (1)/(9)`
or `1 - 2 sin^(2) theta = 9`
or `1 - 2x^(2) = (1)/(9)`
or `x^(2) = (4)/(9)`
or `x = +-(2)/(3)`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.2|6 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

If cos(2sin^(-1)x)=(1)/(9), then find the values of x.

If cos^(-1) x = (pi)/(3) , the find the value of sin ^(-1)x .

If sin ^(-1) x =(pi)/(4) , find the value of cos^(-1) x .

If sin(sin^(-1)(1)/(5)+cos^(-1)x)=1 then find the value of x.

If tan(cos^(-1) x) = sin (cot^(-1).(1)/(2)) , then find the value of x

If sin (sin^(-1).(1)/(5) + cos^(-1) x) = 1 , then find the value of x

If a le 2 sin^(-1)x+cos^(-1)x le b , then find the value of a and b.

If (sin x + cos x)/(sin x - cos x) = (6)/(5) , then the value of (tan^(2) x + 1)/(tan^(2) x-1) is :

If -1<=x,y<=1 such that sin^(-1)x+sin^(-1)y=(pi)/(2), find the value of cos^(-1)x+cos^(-1)y

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Question Bank
  1. If cos (2 sin^(-1) x) = (1)/(9), then find the value of x

    Text Solution

    |

  2. If alpha and beta are the two zeroes of the equation 3 cos ^-1(...

    Text Solution

    |

  3. If log pi x gt 0 then the absolute value of log 1/pi(sin ^-1 (2 x)/...

    Text Solution

    |

  4. If sin ^-1(sin 4)^-1+cos ^-1(cos 8)+tan ^-1(tan 6)+cot ^-1 .(cot 10)=...

    Text Solution

    |

  5. Total number of ordered pairs (x, y) satisfying |y|=cos x and y=sin...

    Text Solution

    |

  6. Find the number of points x in[-pi/2, (3 pi)/2] satisfying the equ...

    Text Solution

    |

  7. If the equation sin ^-1(x^2+x+1)+cos ^-1(lambda x+1)=pi/2 has exactly ...

    Text Solution

    |

  8. Number of values of x satisfying the equation cos ^-1(x^2-.5 x+6)=...

    Text Solution

    |

  9. Given f(x)=tan ^-1(cot x)+cot ^-1(tan x),(pi/2 lt x lt pi) , then ...

    Text Solution

    |

  10. If all the roots of the equation x^3-3 x=0 satisfy the equation (alpha...

    Text Solution

    |

  11. If the solution set of inequality (cosec^-1 x^2)-2 cosec^-1 x ge pi/6(...

    Text Solution

    |

  12. Find the sum of the values of x satisfying the equation tan ^-1((2 ...

    Text Solution

    |

  13. Number of values of x satisfying the equation cos ((4 pi)/3-cos ^-1...

    Text Solution

    |

  14. If the value of expression sin ^-1(sin 2013^(circ))+cos ^-1(cos.2013^...

    Text Solution

    |

  15. Let f:[0,3 pi] rarr[-pi/2, pi/2] be defined by f(x)=sin ^-1(sin x)...

    Text Solution

    |

  16. function f(x)=(arccot x/2+operatornamearccot x/3)/(arctan x/2+arctan ...

    Text Solution

    |

  17. If m and M are the least and the greatest value of (cos ^-1 x)^2...

    Text Solution

    |

  18. Solution of the equation cot (overset (4) underset (r =1) sum cot ^-1...

    Text Solution

    |

  19. If the equation sin ^-1 x=cosec^-1 x is satisfied for alpha and beta, ...

    Text Solution

    |

  20. Let f(x)=sin ^5 x-cos ^2 x and g(x)=cot ^-1(x^2+x+1) . Number of...

    Text Solution

    |

  21. The value of 3 sin (1/2 arc cos 1/9) +4 cos (1/2 arc cos 1/8) equal t...

    Text Solution

    |