Home
Class 12
MATHS
If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=al...

If `"sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)/(ab) "cos" alpha+y^2/b^2 ="sin"^2 alpha`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPER-4

    SHARAM PUBLICATION|Exercise EXERCISE|41 Videos

  • QUESTION PAPER 2010

    SHARAM PUBLICATION|Exercise EXERCISE|53 Videos

Similar Questions

Explore conceptually related problems

If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)/(ab) "cos" theta +y^2/b^2 ="sin"^2 theta.

If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "cos" theta +4y^2 =36 "sin"^2 theta .

If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^4 +4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)

If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 , then prove that a^(2) cos^(2) alpha + b^(2) sin^(2) alpha = p^(2) .

If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)) , then prove that b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4)) +a^(2)y^(2)=c^(4)

If y =(sin^(-1) x)^2 , prove that (1-x^2)y_2 - xy_1 - 2 = 0

SHARAM PUBLICATION-MODEL QUESTION PAPER-5-EXERCISE
  1. Find the value of a such that the function f defined by f(x)={((sinax...

    Text Solution

    |

  2. Differentiate tan^(-1) frac (sqrt(1+x^2) + sqrt(1-x^2))(sqrt(1+x^2) ...

    Text Solution

    |

  3. If y = (sinx)^x find (dy)/(dx).

    Text Solution

    |

  4. Find the points on the curve y = x^3 - 11x + 5 at which the equation o...

    Text Solution

    |

  5. Evaluate intx/((x^2 + 4)) dx.

    Text Solution

    |

  6. Evaluate int(0)^(pi//4)log(1+tanx)dx.

    Text Solution

    |

  7. Evaluate int(sinx + cosx)/(sqrt(sin2x))dx

    Text Solution

    |

  8. Solve dy + e^-y sin x dx = 0.

    Text Solution

    |

  9. If the sum of two unit vectors is a unit vectors find the magnitude of...

    Text Solution

    |

  10. Find a vector of magnitude 5 units and parallel to the resultant of ve...

    Text Solution

    |

  11. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

    Text Solution

    |

  12. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

    Text Solution

    |

  13. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

    Text Solution

    |

  14. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

    Text Solution

    |

  15. Using properties of determinants, prove the following abs{:(a^2, bc, a...

    Text Solution

    |

  16. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

    Text Solution

    |

  17. int(pi//6)^(pi//3)dx/(1+sqrtcotx)

    Text Solution

    |

  18. Solve the differential equation (x^(2)+1)(dy)/(dx)+2xy= sqrt(x^(2)+4),

    Text Solution

    |

  19. Find a unit vector perpendicular to both of the vectors veca + vecb an...

    Text Solution

    |

  20. Find the equations of the plane passing through the point (2, 1, 3) an...

    Text Solution

    |