Home
Class 12
MATHS
If 0 lt x lt 1", then " sqrt(1+x^(2))[...

If `0 lt x lt 1", then " sqrt(1+x^(2))[{x cos (cot^(-1)x) + sin ( cot^(-1) x)}^(2) -1]^(1//2) ` is equal to

A

`( x )/( sqrt( 1+ x^(2)))`

B

x

C

`x sqrt( 1+ x^(2))`

D

`sqrt( 1+ x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRY RATIOS AND IDENTITIES

    ML KHANNA|Exercise PROBLEM SET (2) TRUE AND FALSE|4 Videos

  • TRIGONOMETRY RATIOS AND IDENTITIES

    ML KHANNA|Exercise PROBLEM SET (3) ( MULTIPLE CHOICE QUESTIONS)|23 Videos

  • TRIGONOMETRY RATIOS AND IDENTITIES

    ML KHANNA|Exercise PROBLEM SET (1) FILL IN THE BLANKS|2 Videos

  • TRIGONOMETRICAL EQUATIONS

    ML KHANNA|Exercise SELF ASSESSMENT TEST |27 Videos

Similar Questions

Explore conceptually related problems

If 0

If 0ltxlt1 then sqrt(1+x^(2))[{x cos (cot^(-1)x)+sin(cot^(-1)x}^(2)-1]^(1/2)

If [ x cos ( cot^(-1) x ) + sin ( cot^(-1) x) ]^(2) = (51)/(50) then the positive value of x is

If -1 lt x lt 0 then sin^(-1) x equals-

If -1 lt x lt 0 , then cos^(-1) x is equal to

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))

Lt_(x rarr1)(1-sqrt(x))/((cos^(-1)x)^(2)) is equal to

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

ML KHANNA-TRIGONOMETRY RATIOS AND IDENTITIES-PROBLEM SET (2) ( MULTIPLE CHOICE QUESTIONS)
  1. If a cos theta - b sin theta = lambda, then AA real theta

    Text Solution

    |

  2. sqrt( 3) sin x + cos x is maximum when x is

    Text Solution

    |

  3. The set of values of 'a' for which the equation sqrt(a) "cos" x -2 "...

    Text Solution

    |

  4. Given 12 sin theta + 5 cos theta =2 x^(2) - 8 x +21 and theta and x a...

    Text Solution

    |

  5. If cos 25^(@) + sin 25^(@) =0, then: cos 50^(@)=

    Text Solution

    |

  6. The equation sin x ( sin x + cos x ) = k has real solution if and only...

    Text Solution

    |

  7. The maximum value of 12 sin theta -9 sin ^(2) theta is

    Text Solution

    |

  8. cos2 theta+2 costheta is always

    Text Solution

    |

  9. If l,g are the least and greatest values of 9 cos 2theta - 24 cos thet...

    Text Solution

    |

  10. The ratio of the greatest value of 2-cos x+s in^2x to its least value ...

    Text Solution

    |

  11. If cos A = 3/4 then the value of 32sin( A/2)* sin (5A/2) is.

    Text Solution

    |

  12. The value of sin^3 10^0+sin^3 50^0-sin^3 70^0 is equal to -3/2 (b) 3/...

    Text Solution

    |

  13. If y = 4sin ^(2) theta - cos 2 theta, then y lies in the interval

    Text Solution

    |

  14. If x = ( 4 lambda)/( 1+ lambda^(2)) and y = ( 2 - 2 lambda^(2))/( 1+ ...

    Text Solution

    |

  15. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |

  16. The given expression sec^2 theta =(4xy)/((x+y)^(2)) is true if and onl...

    Text Solution

    |

  17. If sin x + sin y = 3 ( cos y - cos x ), then the value of sin 3x + si...

    Text Solution

    |

  18. If A+B+C= pi ( A,B,C gt 0) and the angle C is obtuse, then

    Text Solution

    |

  19. If sin(x+3 alpha)=3sin (alpha-x) then

    Text Solution

    |

  20. If 0 lt x lt 1", then " sqrt(1+x^(2))[{x cos (cot^(-1)x) + sin ( cot...

    Text Solution

    |