Home
Class 12
MATHS
If a,b,c are real positive numbers and t...

If a,b,c are real positive numbers and `theta =tan^(-1)[(a(a+b+c))/(bc)]^(1/2)+tan^(-1)[(b(a+b+c))/(ca)]^(1/2)+tan^(-1)[(c(a+b+c))/(ab)]^(1/2)`, then `tantheta` equals

A

0

B

1

C

`(a+b+c)/(abc)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - C)(OBJECTIVE TYPE QUESTIONS (MORE THAN ONE OPTIONS ARE CORRECT))|13 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - D)(LINKED COMPREHENSION TYPE QUESTIONS)|9 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - A)(OBJECTIVE TYPE QUESTIONS (ONE OPTION IS CORRECT))|45 Videos
  • INTEGRALS

    AAKASH INSTITUTE|Exercise Try yourself|50 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - j|3 Videos

Similar Questions

Explore conceptually related problems

If a,b,c be positive real numbers and the value of theta=tan^(-1)sqrt((a(a+b+c))/(bc))+tan^(-1)sqrt((b(a+b+c))/(ca))+tan^(-1)sqrt((c(a+b+a))/((ab))) then tan theta is equal to

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) = pi

If a,b,c are positive real numbers,then (1)/(log_(a)bc+1)+(1)/(log_(b)ca+1)+(1)/(log_(c)ab+1)=

If a,b, and c are distinct positive real numbers and a^(2)+b^(2)+c^(2)=1, then ab+bc+ca is

If a, b, c are positive real numbers then (1)/("1+log"_(a)bc) + (1)/("1+log"_(b)ca) +(1)/("1+log"_(c)ab)=

If a,b,c>0 and s=(a+b+c)/(2), prove thattan^(-1)sqrt((2as)/(bc))+tan^(-1)sqrt((2bs)/(ca))+tan^(-1)sqrt((2cs)/(ab))=pi

For any positive real number x;write the value of {(x^(a))^(b)}^((1)/(ab)){(x^(b))^(c)}^((1)/(bc)){(x^(c))^(a)}^((1)/(ca))

AAKASH INSTITUTE-INVERSE TRIGONOMETRIC FUNCTIONS-ASSIGNMENT (SECTION - B)(OBJECTIVE TYPE QUESTIONS (ONE OPTION IS CORRECT))
  1. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi, then 1/(xy)+1/(yz)+1/(zx)=

    Text Solution

    |

  2. The value of tan^(-1)1+tan^(-1)2+tan^(-1)3 is

    Text Solution

    |

  3. If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)...

    Text Solution

    |

  4. Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

    Text Solution

    |

  5. If alpha= tan^-1 ((sqrt3 x)/(2lamda-x)), beta= tan^-1 ((2x-lamda)/(lam...

    Text Solution

    |

  6. The value of tan[1/2cos^(-1).sqrt5/3] is

    Text Solution

    |

  7. If -1 le x le -1/2, then sin^(-1)(3x-4x^3) equals

    Text Solution

    |

  8. The value of cos (2Cos^-1 0.8) is

    Text Solution

    |

  9. Find the value of 4 tan^-1 (1/5) - tan^-1 (1/239)

    Text Solution

    |

  10. cot^(-1)(sqrtcosalpha)-tan^(-1)(sqrt(cosalpha))=x, x, ge 0, then sin x...

    Text Solution

    |

  11. If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

    Text Solution

    |

  12. The set of values of x satisfying |sin^(- 1)x|lt|cos^(- 1)x|,is

    Text Solution

    |

  13. Let f(x)=sec^-1(x-10)+cos^-1(10-x). Then range of f(x) is

    Text Solution

    |

  14. Let f(x) = cosec^-1[1 + sin^2x], where [*] denotes the greatest intege...

    Text Solution

    |

  15. The sum sum (n=1)^ootan^(-1)(1/(2^n+2^(1-n))) equals

    Text Solution

    |

  16. The expression tan.(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x) equals

    Text Solution

    |

  17. The sum sum(k=1)^oocot^(-1)(2k^2) equals

    Text Solution

    |

  18. The sum tan^(-1).(1)/(1+x+x^2)+tan^(-1).(1/(3+3x+x^2))+tan^(-1).(1/(7+...

    Text Solution

    |

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

    Text Solution

    |

  20. If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible v...

    Text Solution

    |