Home
Class 11
MATHS
If cottheta+tantheta=x and sectheta-cos...

If `cottheta+tantheta=x` and `sectheta-costheta=y ,` prove that `(x^2y)^(2/3)-(x y^2)^(2/3)=1`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If x=sectheta- tantheta"and " y=cosec theta +cottheta , then prove that xy+1=y-x .

If:x/a costheta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2

If x=sectheta-tantheta and y=cos e ctheta+cottheta, then prove that x y+1=y-xdot

Prove that if x=a(costheta+sin thetasin2theta) and y=a(sintheta+costhetasin2theta) ,then show that (x+y)^(2//3)+(x-y)^(2//3)=2a^(2//3)

(2x-y)^(3)-(x+y)^(3)+(2y-x)^(3)

If x=a(costheta+sinthetasin2theta)andy=a(sintheta+costhetasin2theta) , then show that (x+y)^((2)/(3))+(x-y)^((2)/(3))=2a^((2)/(3)) .

If tantheta+sectheta=e^x then costheta equals

x=sectheta-costheta , y=sec^n theta- cos^n theta show that (dy/dx)^2=(n^2(y^2+4))/(x^2+4)

If x^2=y^3 , then prove that (x/y)^(3/2)+(y/x)^-(2/3)=x^(1/2)+y^(1/3) .

If x+iy=2/(3+costheta+isintheta) ,show that 2x^2+2y^2=3x-1

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Three circle touch one another externally. The tangents at their point...

    Text Solution

    |

  2. Prove that tan20^0tan40^0tan80^0=tan60^0

    Text Solution

    |

  3. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

    Text Solution

    |

  4. The solution of the system of equations sinxsiny=(sqrt(3))/4,cosxcosy=...

    Text Solution

    |

  5. Find the least value of sec A+secB+secC in an acute angled triangle

    Text Solution

    |

  6. In triangle ABC if cosAcosB +sinAsinB sinC=1 then prove that a:b:c=1:1...

    Text Solution

    |

  7. Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real numbe...

    Text Solution

    |

  8. Number of values of p for which equation sin^3x+1+p^3-3 p sinx=0 (p >0...

    Text Solution

    |

  9. In A B C , prove that cosA+cosB+cosClt=3/2dot

    Text Solution

    |

  10. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

    Text Solution

    |

  11. If pcos e ctheta+qcottheta=2 and p^2cos e c^2theta-q^2cot^2theta=5 t...

    Text Solution

    |

  12. If a, b and c are in G.P. then prove that <math xmlns="http://www.w3...

    Text Solution

    |

  13. In triangle ABC tan(A/2), tan(B/2) and tan (C/2) are in A.P. then prov...

    Text Solution

    |

  14. In triangleABC (b+c)/11=(c+a)/12=(a+b)/13 then prove that (cosA)/7=(co...

    Text Solution

    |

  15. alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, resp...

    Text Solution

    |

  16. Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n...

    Text Solution

    |

  17. If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equi...

    Text Solution

    |

  18. Let alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot Then prove that sq...

    Text Solution

    |

  19. In DeltaABC, if BC is unity, sin(A/2)=x1,sin(B/2)=x2,cos(A/2)=x3,cos(B...

    Text Solution

    |

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

    Text Solution

    |