Home
Class 11
MATHS
The product of the sines of the angles o...

The product of the sines of the angles of a triangle is `p` and the product of their cosines is `qdot` Show that the tangents of the angles are the roots of the equation `q x^3-p x^2+(1+q)x-p=0.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Find the cubic equation whose roots are the squares of the roots of the equation x^3 +p_1 x^2 +p_2 x+p_3 =0

Find p, where p,q belongs to R If p and q are the roots of equation x^2-px+q=0 then p=,

What is the angle between P and Q the cross product of (P+Q)and (P-Q) ?

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that p+q=0 . Also, show that their other roots are the roots of the equation x^2+x+p q=0.

If p and q are the roots of x^2 + px + q = 0 , then find p.

If p , qr are real and p!=q , then show that the roots of the equation (p-q)x^2+5(p+q)x-2(p-q=0 are real and unequal.

If alpha,beta are the roots of the equation x^2+p x+q=0,t h e n-1/alpha,-1/beta are the roots of the equation (a) x^2-p x+q=0 (b) x^2+p x+q=0 (c) q x^2+p x+1=0 (d) q x^2-p x+1=0

If p ,q are real p!=q , then show that the roots of the equation (p-q)x^2+5(p+q)x-2(p-q)=0 are real and unequal.

In a triangle PQR angle R=(pi)/(4), if tan (p/3) and tan ((Q)/(3)) are the roots of the equation ax ^2 + bx +c=0 then

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If in a triangle A B C ,(1+cosA)/a+(1+cosB)/b+(1+cosC)/c =(k^2(1+cosA...

    Text Solution

    |

  2. Solve tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3)

    Text Solution

    |

  3. The product of the sines of the angles of a triangle is p and the prod...

    Text Solution

    |

  4. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

    Text Solution

    |

  5. In A B C ,a=5,b=12 ,c=90^0a n dD is a point on A B so that /B C D=45^...

    Text Solution

    |

  6. Solve tan5theta=cot2theta

    Text Solution

    |

  7. If x+y+z=pi/2, then prove that |[sinx,siny,sinz],[cosx,cosy,cosz],[c...

    Text Solution

    |

  8. In a right-angled isosceles triangle, the ratio of the circumradius an...

    Text Solution

    |

  9. If sinx+cos e cx=2, then sin^n x+cos e c^n x is equal to 2 (b) 2^n ...

    Text Solution

    |

  10. Solve 2sin^(2)x-5sinxcosx-8cos^2x=-2

    Text Solution

    |

  11. Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

    Text Solution

    |

  12. In A B C ,(sinA(a-bcosC))/(sinC(c-bcosA) = (a) -2 (b) -1 (c) 0 (d...

    Text Solution

    |

  13. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+s...

    Text Solution

    |

  14. Prove that cos20^0cos40^0cos60^0cos80^0=1/(16)dot

    Text Solution

    |

  15. Find common roots of the equations 2sin^2x+sin^2 2x=2a n dsin2x+cos2x=...

    Text Solution

    |

  16. The sides of a triangle are in A.P. and its area is 3/5t h of the an e...

    Text Solution

    |

  17. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0ltxltpi, then xis ...

    Text Solution

    |

  18. If K=sin(pi/(18))sin((5pi)/(18))sin((7pi)/(18)), then the numerical va...

    Text Solution

    |

  19. One of the general solutions of 4sin^4x+cos^4x=1 is

    Text Solution

    |

  20. The value of the expression (tan^2 20^0-sin^2 20^0)/(tan^2 20^0+sin^2 ...

    Text Solution

    |