Home
Class 12
MATHS
The number of solutions of the equation ...

The number of solutions of the equation `tan^(-1)(1+x)+tan^(-1)(1-x)=pi/2` is 2 (b) 3 (c) 1 (d) 0

A

2

B

3

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
`tan^(-1) (1 + x) + tan^(-1) (1- x) = (pi)/(2)`
or `tan^(-1) (1 + x) = (pi)/(2) - tan^(-1) (1 -x)`
`= cot^(-1) (1 -x)`
`= tan^(-1) ((1)/(1 -x))`
or `1 + x = (1)/(1 -x)`
or `1 - x^(2) = 1`
or `x = 0`
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

The number of solution of the eqution tan^(-1)2x+tan^(-1)3x=(pi)/(4) is

Solve the equation tan^(-1)2x+tan^(-1)3x=pi/4

The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1)x=pi/2+sin^(-1)x is 0 (b) 1 (c) 2 (d) 3

The number of solution of the equation |tan^(-1)|x||=sqrt((x^(2)+1)^(2)-4x^(2)) is

Find the number of solution of the eqution tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)(3x)

The number of solutions of equations |tan2x|=sin x" in"[0,pi]

The number of solution of the equation 2sin^(-1)((2x)/(1+x^(2)))-pi x^(3)=0 is equal to

Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w h e r e n >0,m<=0, is 3 (b) 1 (c) 2 (d) None of these

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1...

    Text Solution

    |

  2. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

    Text Solution

    |

  3. The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi...

    Text Solution

    |

  4. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

    Text Solution

    |

  5. If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y...

    Text Solution

    |

  6. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

    Text Solution

    |

  7. The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(...

    Text Solution

    |

  8. If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is ...

    Text Solution

    |

  9. sum(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1))))i se q u a lto ...

    Text Solution

    |

  10. sum(m-1)^ntan^(-1)((2m)/(m^4+m^2+2)) is equal to (a) tan^(-1)((n^...

    Text Solution

    |

  11. The value of tan^(-1)4/7+tan^(-1)4/(19)+tan^(-1)4/(39)+tan^(-1)4/(67)+...

    Text Solution

    |

  12. The sum of series sec^(-1)sqrt(2)+sec^(-1)(sqrt(10))/3+sec^(-1)(sqrt(5...

    Text Solution

    |

  13. If sin theta=3/5, then cos theta=?

    Text Solution

    |

  14. The value 2tan^(-1)[sqrt((a-b)/(a+b))tantheta/2] is equal to (a)cos^(-...

    Text Solution

    |

  15. If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x i...

    Text Solution

    |

  16. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

    Text Solution

    |

  17. If x1=2tan^(-1)((1+x)/(1-x)),x2=sin^(-1)((1-x^2)/(1+x^2)) , where x in...

    Text Solution

    |

  18. If the equation x^3+b x^2+c x+1=0,(bltc), has only one real root alpha...

    Text Solution

    |

  19. The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to sin^...

    Text Solution

    |

  20. If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal t...

    Text Solution

    |