Home
Class 12
MATHS
Prove that : cot^(-1)((1+ab)/(a-b))+cot^...

Prove that : `cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1+ca)/(c-a))=pi,(a>b>c>0)`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Prove the followings : "cot"^(-1)(ab+1)/(a-b)+"cot"^(-1)(bc+1)/(b-c)+"cos"^(-1)(ca+1)/(c-a)=pi(agtbgtc)

Prove that : cot(pi/4-2cot^(-1)3)=7

Prove that : 2"cot"^(-1)1/3+"tan"^(-1)3/4=pi .

Prove that sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

Prove the following : 2cot^(-1)(2)+cosec^(-1)(5/3)=pi/2

If the points (a^3/(a-1),(a^2-3)/(a-1)) , (b^3/(b-1),(b^2-3)/(b-1)) , (c^3/(c-1),(c^2-3)/(c-1)) are collinear for 3 distinct values a,b,c and a!=1, b!=1, c!=1 , then find the value of abc-(ab+bc+ca)+3(a+b+c) .

Prove that cos((3pi)/(2)+x)cos(2pi+x)[cot((3pi)/(2)-x)+cot(2pi+x)]=1

Prove the followings : cot^(-1)((sqrt(1+x^(2))-1)/x)=pi/2-1/2tan^(-1)x

In triangle ABC, prove that, tan((B-C)/(2))=(b-c)/(b+c)cot((A)/(2)) tan((C-A)/(2))=(c-a)/(c+a)cot((B)/(2)) tan((A-B)/(2))=(a-b)/(a+b)cot((C)/(2))

ALLEN -INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. the value of 3tan^- 1(1/4)+tan^- 1(1/20)+tan^- 1(1/1985)

    Text Solution

    |

  2. If sin^2x + sin^2y < 1 ; x, y in R then prove that sin^-1(tanx . tany...

    Text Solution

    |

  3. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. 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

    |

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

    Text Solution

    |