Home
Class 11
MATHS
The base of a triangle is divided into t...

The base of a triangle is divided into three equal parts. If `t_1, t_2,t_3` are the tangents of the angles subtended by these parts at the opposite vertex, prove that `(1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If A, B, C, be the centres of three co-axial circles and t_(1),t_(2),t_(3) be the lengths of the tangents of them any piont, prove that bar(BC).t_(1)^(2)+bar(CA).t_(2)^(2)+bar(AB).t_(3)^(2)=0

If t_(1),t_(2),t_(3) are the feet of normals drawn from (x_(1),y_(1)) to the parabola y^(2)=4ax then the value of t_(1)t_(2)t_(3) =

Show that the area formed by the normals to y^2=4ax at the points t_1,t_2,t_3 is

Area of the triangle formed by the threepoints 't_1'. 't_2' and 't_3' on y^2=4ax is K|(t_1-t_2) (t_2-t_3)(t_3-t_1)| then K=

If the chord joining the points t_1 and t_2 on the parabola y^2 = 4ax subtends a right angle at its vertex then t_1t_2=

If the tangents at t_(1) and t_(2) on y^(2) = 4ax makes complimentary angles with axis then t_(1)t_(2) =

Write the equation of a tangent to the curve x=t, y=t^2 and z=t^3 at its point M(1, 1, 1): (t=1) .

If the normal at point 't' of the curve xy = c^(2) meets the curve again at point 't'_(1) , then prove that t^(3)* t_(1) =- 1 .

If the normals at points t_1 and t_2 meet on the parabola, then (a) t_1t_2=1 (b) t_2=-t_1-2/(t_1) (c) t_1t_2=2 (d) none of these

The normal drawn at a point (a t_1^2,-2a t_1) of the parabola y^2=4a x meets it again in the point (a t_2^2,2a t_2), then t_2=t_1+2/(t_1) (b) t_2=t_1-2/(t_1) t_2=-t_1+2/(t_1) (d) t_2=-t_1-2/(t_1)

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Express 45^0 20 ' 10 ' ' in radian measure (pi=3. 1415)

    Text Solution

    |

  2. The number of solution of sec^2theta+cos e c^2theta+2cos e c^2theta=8,...

    Text Solution

    |

  3. The base of a triangle is divided into three equal parts. If t1, t2,t3...

    Text Solution

    |

  4. A man observes when he has climbed up 1/3 of the length of an inclined...

    Text Solution

    |

  5. Number of solutions of the equation sin^4x-cos^2xsinx+2sin^2x+sinx=0in...

    Text Solution

    |

  6. If the median AD of triangle ABC makes an angle pi/4 with the side BC,...

    Text Solution

    |

  7. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4thet...

    Text Solution

    |

  8. The value of k if the equation 2 cos x + cos 2kx=3 has only one soluti...

    Text Solution

    |

  9. If I1, I2, I3 are the centers of escribed circles of triangle A B C ,...

    Text Solution

    |

  10. Let f(theta)=1/(1+(cottheta)^2) , and S=sum(theta=1^0)^(89^0)f(theta),...

    Text Solution

    |

  11. The number of values of theta in the interval (-pi/2,pi/2) satisfying ...

    Text Solution

    |

  12. If the distance between incenter and one of the excenter of an equi...

    Text Solution

    |

  13. The value of 3(sin^4t+cos^4t-1)/(sin^6t+cos^6t-1) is equal to

    Text Solution

    |

  14. Number of roots of the equation 2^(tan(x-pi/4))-2(0. 25)^((sin^2(x-pi...

    Text Solution

    |

  15. If sintheta-costheta=1, then the value of sin^3theta-cos^3theta is

    Text Solution

    |

  16. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

    Text Solution

    |

  17. The smallest positive value of x (in radians) satisfying the equation...

    Text Solution

    |

  18. In convex quadrilateral A B C D ,A B=a ,B C=b ,C D=c ,D A=d . This qua...

    Text Solution

    |

  19. Suppose that for some angles xa n dy , the equations sin^2x+cos^2y=(3a...

    Text Solution

    |

  20. The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=...

    Text Solution

    |