Home
Class 12
MATHS
If alpha=2 tan^(-1)((1+x)/(1-x)) and ...

If `alpha=2 tan^(-1)((1+x)/(1-x)) and beta= sin^(-1)((1-x^2)/(1+x^2))` for `0 lt x lt 1` ,then prove that `alpha+beta =pi` , what the value of `alpha+beta` will be if `x gt 1`.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) in the following y= sin^(-1) ((1-x^(2))/(1+ x^(2))), 0 lt x lt 1

If alpha+beta=(pi)/(4) , then the value of (1+tanalpha)(1+tanbeta) is

Differentiate sin^(-1)((2x)/(1+x^(2))) w. r. t. tan^(-1)x, -1 lt x lt 1 .

Let -pi/6 beta_1 and alpha_2 >beta_2 , then alpha_1 + beta_2 equals

Prove that, tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/sqrt3

Solve for x : sin^(- 1)(sin((2x^2+4)/(1+x^2)))lt pi-3

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

ALLEN -INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

    Text Solution

    |

  2. Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x) = pi If x satisfies the equa...

    Text Solution

    |

  3. If alpha=2 tan^(-1)((1+x)/(1-x)) and beta= sin^(-1)((1-x^2)/(1+x^2...

    Text Solution

    |

  4. solve:sin^-1x+sin^-1 2x=pi/3

    Text Solution

    |

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

    Text Solution

    |

  6. Solve for x : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

    Text Solution

    |

  7. Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

    Text Solution

    |

  8. Solve the following equation: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

    Text Solution

    |

  9. If 1/2tan^(- 1)((2x)/(x^2-1))+cos^(- 1)((x^2-1)/(x^2+1))=(2pi)/3 the...

    Text Solution

    |

  10. Find the sum of the series :(tan^- 1)1/3+(tan^- 1)2/9+....+(tan^- 1)(2...

    Text Solution

    |

  11. Find the sum to n terms cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+ cot^(-1)...

    Text Solution

    |

  12. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

    Text Solution

    |

  13. Find the domain of definition the following function: f(x)=log(10)(1-l...

    Text Solution

    |

  14. નીયેના બહુવિકલ્પ પ્રશ્નોના જ​વાબ માટે સાયો વિકલ્પ પસંદ કરો: sin^(-1...

    Text Solution

    |

  15. tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=?

    Text Solution

    |

  16. Find the sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(...

    Text Solution

    |

  17. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

    Text Solution

    |

  18. If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > ...

    Text Solution

    |

  19. Solution set of inequality (cot^-1x)^2-5cot^-1x+6>0 is

    Text Solution

    |

  20. Solve the following inequality: sin^(-1) x > cos^(-1) x

    Text Solution

    |