Home
Class 12
MATHS
Let a, b and c be positive real numbers....

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'

A

`pi//4`

B

`pi//2`

C

`pi`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|72 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

If a , b , c >0 and s=(a+b+c)/2 , prove that tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0

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

If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt(b^(-1)\ c)\ xx\ sqrt(c^(-1)a) is equal to: (a)\ 1 (b) a b c (c) sqrt(a b c) (d) 1/(a b c)

Prove that tan^(-1)((a-b)/(1+ab))+ tan^(-1)((b-c)/(1+bc))+tan^(-1)((c-a)/(1+ca))=0 , ab>(-1), bc>(-1), ca>(-1)

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

Prove that 2tan^(-1)(sqrt((a-b)/(a+b))tan(theta/2))=cos^(-1)((acostheta+b)/(a+bcostheta))

prove that 2tan^-1(sqrt((a-b)/(a+b))tan(theta/2)) = cos^-1((acostheta+b)/(a+bcostheta))

Prove that (1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab))) , where a,b,c gt 0

OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. Two angles of a triangle are cot^-1 2 and cot^-1 3, then the third ang...

    Text Solution

    |

  2. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

    Text Solution

    |

  3. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

    Text Solution

    |

  4. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) the value of x^(100)+y^(10...

    Text Solution

    |

  5. The value of (alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1) ((alpha)/(bet...

    Text Solution

    |

  6. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

    Text Solution

    |

  7. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

    Text Solution

    |

  8. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

    Text Solution

    |

  9. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

    Text Solution

    |

  10. Which of the following angles is greater? theta1=sin^(-1)+sin^(-1)1/3o...

    Text Solution

    |

  11. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

    Text Solution

    |

  12. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

    Text Solution

    |

  13. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

    Text Solution

    |

  14. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

    Text Solution

    |

  15. Show that: cos(2tan^(-1)1/7)=sin(4^(-1)1/3)

    Text Solution

    |

  16. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

    Text Solution

    |

  17. cos{cos^(-1)(-1/7)+sin^(-1)(-1/7)} =

    Text Solution

    |

  18. If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal ...

    Text Solution

    |

  19. Evaluate: sin(1/2cos^(-1)4/5)

    Text Solution

    |

  20. If xge0 and theta=sin^(-1)x+cos^(-1)x-tan^(-1)x, then

    Text Solution

    |