Home
Class 11
MATHS
A tower P Q stands at a point P within t...

A tower `P Q` stands at a point `P` within the triangular park `A B C` such that the sides `a , ba n dc` of the triangle subtend equal angles at `P ,` the foot of the tower. if the tower subtends angles `alpha,betaa n dgamma,a tA , Ba n dC` respectively, then prove that `a^2(cotbeta-cotgamma)+b^2(cotgamma-cotalpha)+a^2(cotalpha-cotbeta)=0`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are alpha,betaa n dgamma then prove that r^2=(alphabetagamma)/(alpha+beta+gamma)

A vertical tower PQ subtends the same anlgle of 30^@ at each of two points A and B ,60 m apart on the ground .If AB subtends an angle of 120^@ at P the foot of the tower ,then find the height of the tower .

A tower of height b subtends an angle at a point 0 on the ground level through the foot of the tower and at a distance a from the foot of the tower. A pole mounted on the top of the tower also subtends an equal angle at 0. The height of the pole is

P is a point on the line y+2x=1, and Qa n dR two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

In A B C , right-angled at C , if tanA=sqrt((sqrt5-1)/2) , show that the sides a , ba n dc are in G.P.

At a distance 2h m from the foot of a tower of height h m the top of the tower and a pole at the top of the tower subtend equal angles. Prove that the height of the pole should be (5h)/(3) m.

If the first and the n^("th") term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

PQR is a triangular park with PQ=PR=200m . A T.V tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P , Q and R respectively 45^@ , 30^@ and 30^@ then the height of the tower in m is

Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b : c be sqrt(3):sqrt(2) . Find angle Adot

If the first and the nth terms of a G.P are a and b , respectively, and if P is the product of the first n terms then prove that P^2=(a b)^ndot

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that cos36^0cos72^0cos108^0cos144^0=1/(16)dot

    Text Solution

    |

  2. The equation tan^4x-2sec^2x+a=0 will have at least one solution if

    Text Solution

    |

  3. A tower P Q stands at a point P within the triangular park A B C such ...

    Text Solution

    |

  4. The number of ordered pairs (x,y) satisfying |x|+|y|=2 and sin""((pi...

    Text Solution

    |

  5. If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin...

    Text Solution

    |

  6. Prove that a(bcosC-c cosB)=b^2-c^2

    Text Solution

    |

  7. If 4sin^4x+cos^4x=1,then x is equal to (n in Z) (a)npi (b) npi+-...

    Text Solution

    |

  8. If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/...

    Text Solution

    |

  9. If in a triangle acos^2(C/2)+ c cos^2(A/2)=(3b)/2, then find the rela...

    Text Solution

    |

  10. Evaluate cosacos2acos3a......... cos 999 a , where a=(2pi)/(1999)dot

    Text Solution

    |

  11. If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z)

    Text Solution

    |

  12. Let ABC be a triangle of area 24sq.units and PQR be the triangle forme...

    Text Solution

    |

  13. Find the number of pairs of integer (x , y) that satisfy the followin...

    Text Solution

    |

  14. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

    Text Solution

    |

  15. Let A D be a median of the A B Cdot If A Ea n dA F are medians of ...

    Text Solution

    |

  16. Find the value of cos12^0+cos84^0+cos156^0+cos132^0

    Text Solution

    |

  17. If no solution of 3siny+12sin^3x=a lies on the line y=3x , then a in ...

    Text Solution

    |

  18. If in a triangle P Q R ,sinP ,sinQ ,sinR a r e i n AdotPdot , then ...

    Text Solution

    |

  19. Find the angle theta whose cosine is equal to its tangent.

    Text Solution

    |

  20. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |