Home
Class 11
MATHS
In A B C , if b^2+c^2=2a^2, then value ...

In ` A B C ,` if `b^2+c^2=2a^2,` then value of `(cotA)/(cotB+cotC)` is `1/2` (b) `3/2` (c) `5/2` (d) `5/2`

Text Solution

Verified by Experts

Let `tanA = 3k, tanB = 4k, tanC = 5k`
As, `A+B+C = pi`
`:. tanA+tanB+tanC = tanAtanBtanC`
`=>3k+4k+5k = 3k*4k*5k`
`=>12k = 60k^3`
`=>k^2 = 1/5`
`=> k = 1/sqrt5`
`:. tan A = 3/sqrt5, tanB = 4/sqrt5, tanC = 5/sqrt5 = sqrt5`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

In A B C , if cotA+cotB+cotC=0 then find the value of cosAcos BcosC

If in A B C ,A C is double of A B , then the value of cot(A/2)cot((B-C)/2) is equal to 1/3 (b) -1/3 (c) 3 (d) 1/2

The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) 5

In A B C ,(cot A/2+cotB/2)(asin^2B/2+bsin^2A/2)= cotC (b) ccotC (c) cotC/2 (d) ccotC/2

In triangle A B C , if r_1=2r_2=3r_2, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In triangle A B C , if cotA *cotC=1/2a n dcot B* cotC=1/(18), then the value of tanC is

Let Aa n dB are events of an experiment and P(A)=1//4, P(AuuB)=1//2, then value of P(B//A^c) is a. 2//3 b. 1//3 c. 5//6 d. 1//2

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

In A B C ,cotA/2+cotB/2+cotC/2 is equal to Delta/(r^2) (b) ((a+b+c)^2)/(a b c)2R (c) Delta/r (d) Delta/(R r)

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, p...

    Text Solution

    |

  2. If in a triangleA B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a) ...

    Text Solution

    |

  3. In A B C , if b^2+c^2=2a^2, then value of (cotA)/(cotB+cotC) is 1/2 ...

    Text Solution

    |

  4. Let tanx-tan^2x >0 and |2s inx|<1 . Then the intersection of which of ...

    Text Solution

    |

  5. One angle of an isosceles triangle is 120^0 and the radius of its inci...

    Text Solution

    |

  6. If cot^(2)x=cot(x-y)*cot(x-z), then cot2x is equal to (x!= pm pi/4)

    Text Solution

    |

  7. If x+y=pi/4a n dtanx+tany=1,t h e n(n in Z) (a)sinx=0a l w a y s ...

    Text Solution

    |

  8. Prove that (cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2

    Text Solution

    |

  9. If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2 , where x , y , in (0,pi/2), ...

    Text Solution

    |

  10. If 0lt=xlt=2pi, then 2^(cosec^2(x)) sqrt(1/2y^2-y+1)lt=sqrt(2) (a...

    Text Solution

    |

  11. If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y+1) is eq...

    Text Solution

    |

  12. If cos(x+pi/3)+cos x=a has real solutions, then (a) number of inte...

    Text Solution

    |

  13. Solve the equation sin^3x.cos3x+cos^3x.sin3x+3/8=0

    Text Solution

    |

  14. If cos28^0+sin28^0=k^3, t h e ncos17^0 is equal to (a)(k^3)/(sqrt(2)...

    Text Solution

    |

  15. Solve the following system of simultaneous equation for xa n dydot ...

    Text Solution

    |

  16. If (1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)), then alpha is e...

    Text Solution

    |

  17. For the equation 1-2x-x^2=tan^2(x+y)+cot^2(x+y) (a)exactly one valu...

    Text Solution

    |

  18. If tan^2((pi-A)/4)+tan^2((pi-B)/4)+tan^2((pi-C)/4)=1 , then A B C is ...

    Text Solution

    |

  19. For the smallest positive values of xa n dy , the equation 2(sinx+sin...

    Text Solution

    |

  20. The minimum vertical distance between the graphs of y=2+sinx and y=cos...

    Text Solution

    |