Home
Class 12
MATHS
If x in (0, 1), then find the value of t...

If `x in (0, 1)`, then find the value of `tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/(2)`
`tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`
`= (pi)/(2) - tan^(-1) ((2x)/(1 - x^(2))) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))`
`= (pi)/(2) - 2tan^(-1) x + 2tan^(-1) x " " ("as " x in (0, 1))`
`= (pi)/(2)`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

Find the range of tan^(-1)((2x)/(1+x^2))

Find the value of tan [ 1/2 "cosec"^(-1) ((1+x^(2))/(2x)) +1/2 sec^(-1) ((1+x^(2))/(1-x^(2)))]

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

Differentiate tan^(-1)(2x/(1 - x^(2))) with respect to cos^(-1)((1 - x^(2))/(1 + x^(2)))

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

Solve : tan^(-1)((2x)/(1-x^(2)))+cot^(-1)((1-x^(2))/(2x))=(pi)/(3),xgt0

The value of int_(-4)^(4) [ tan^(-1)((x^(2))/( x^(4)+1)) +tan^(-1) ((x^(4)+1)/( x^(2))) ] dx is

The value of int_(0)^(1)(tan^(-1)((x)/(x+1)))/(0tan^(-1)((1+2x-2x^(2))/(2)))dx is

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alp...

    Text Solution

    |

  2. Find the value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4...

    Text Solution

    |

  3. If x in (0, 1), then find the value of tan^(-1) ((1 -x^(2))/(2x)) + co...

    Text Solution

    |

  4. If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

    Text Solution

    |

  5. sin(2sin^(-1) 0.8)=

    Text Solution

    |

  6. cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) is equal to

    Text Solution

    |

  7. The value of sin^(-1)("cot"(sin^(-1)((2-sqrt(3))/4+cos^(-1)(sqrt(12))...

    Text Solution

    |

  8. If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) ...

    Text Solution

    |

  9. If cosec^(-1) (cosec x) and cosec (cosec^(-1) x) are equal function th...

    Text Solution

    |

  10. sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is equal to (a)5 (b) 13 (c) 15...

    Text Solution

    |

  11. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is...

    Text Solution

    |

  12. For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real soluti...

    Text Solution

    |

  13. The number of real solution of the equation tan^(-1) sqrt(x^(2) - 3x +...

    Text Solution

    |

  14. If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then ...

    Text Solution

    |

  15. The number of real solution of the equation sqrt(1+cos2x)=sqrt2 sin^(-...

    Text Solution

    |

  16. Find the set of value of x for which the equation cos^(-1) x + cos^(-1...

    Text Solution

    |

  17. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (pi/4,(3pi)/4) (b) [pi...

    Text Solution

    |

  18. The value of lim(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equ...

    Text Solution

    |

  19. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  20. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

    Text Solution

    |