Home
Class 12
MATHS
Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1...

Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))`, where `|x|<1/(sqrt(3))`. Then a value of y is :

A

`(3x-x^(3))/(1+3x^(2))`

B

`(3x+x^(2))/(1+3x^(2))`

C

`(3x-x^(3))/(1-3x^(2))`

D

`(3x+x^(3))/(1-3x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`tan^(-1)y=tan^(-1)x+tan^(-1)(2x)/(1-x^(2))` ltMbrgt `rarr tan^(-1)y=tan^(-1)x+2 tan^(-1)x=3 tan^(-1)x=tan^(-1)(3x-x^(3))/(1-3x^(22))`
`rarr y=(3x-x^(3))/(1-3x^(2))`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|11 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|72 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

  • LIMITS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1) y = tan^(-1) x + tan^(-1)((2x)/(1 -x^(2)))", where" |x| lt 1/sqrt3 . Then, the value of y is

Prove that tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)((2x)/(2-x^2))

Solve for x : tan^(-1)(2+x)+tan^(-1)(2-x)=tan^(-1)2/3 , where x sqrt(3)

If x gt 1 then 2tan^(-1)x - tan^(-1) ((2x)/(1-x^(2))) =______.

Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(3))/(1-3x^(2)) , |x| lt 1/(sqrt(3))

Solve for x : tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/(79)) , x >0

If y=tan^(-1)(1+2x)+tan^(-1)(1-2x),"then "dy/dx=

tan^(-1)(1/(a-1))=tan^(-1)(1/x)+tan^(-1)((1)/(a^(2)-x+1))

2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equal to

OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. tan(sec^(-1)x )=sin(cos^(-1)(1/sqrt5))

    Text Solution

    |

  2. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

    Text Solution

    |

  3. If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...

    Text Solution

    |

  4. If f(x) =cos^(-1)x+cos^(-1){(x/2+1/2sqrt(3-3x^(2)))} then f(2/3) equ...

    Text Solution

    |

  5. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

    Text Solution

    |

  6. If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = ...

    Text Solution

    |

  7. If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...

    Text Solution

    |

  8. If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=

    Text Solution

    |

  9. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then the value of xsqrt(1-x^(2))+y...

    Text Solution

    |

  10. if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4 ,the...

    Text Solution

    |

  11. The solution set of the equation sin^(-1)x=2 tan^(-1)x is

    Text Solution

    |

  12. If cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))} then x equals

    Text Solution

    |

  13. tan^(-1)(C(1)x-y)/(c(1)+c(3)c(2))+..+tan^(-1)(1)/(c(n)) is equal top

    Text Solution

    |

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

    Text Solution

    |

  15. Sigma(r=1)^(infty) tan^(-1)(1)/(2r^(2))=t then tan t is equal to

    Text Solution

    |

  16. Let (x,y)be such that sin^(-1)(ax)+cos^(-1)y+cos^(-1)(bxy)=(pi)/(2) ...

    Text Solution

    |

  17. Let f:[0,4pi]->[0,pi] be defined by f(x)=cos^-1(cos x). The number ...

    Text Solution

    |

  18. If (sin^(-1)x+sin^(-1)y)(sin^(-1)Z+sin^(-1)w)=pi^(2) and n(1),n(2),n(3...

    Text Solution

    |

  19. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^2+z^4+4x^2y^2z^2=K(x^...

    Text Solution

    |

  20. Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)), where |x|<1/(sqrt(3))....

    Text Solution

    |