Home
Class 12
MATHS
If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1...

If `x=cos^-1(1/(sqrt(1+t^2)))`, `y=sin^-1(1/(sqrt(t^2+1)))` then `dy/dx` is independent of t.

Text Solution

Verified by Experts

The correct Answer is:
`(dy)/(dx)` is independent of `t`.
Promotional Banner

Topper's Solved these Questions

  • VERY SIMILAR TEST 5

    ARIHANT PRAKASHAN|Exercise SECTION C|12 Videos

  • VERY SIMILAR TEST 5

    ARIHANT PRAKASHAN|Exercise SECTION C|12 Videos

  • VERY SIMILAR TEST 4

    ARIHANT PRAKASHAN|Exercise Section - C |13 Videos

  • VERY SIMILAR TEST 6

    ARIHANT PRAKASHAN|Exercise SECTION C ANSWER ANY ONE QUESTIONS|11 Videos

Similar Questions

Explore conceptually related problems

If sin y=(2t)/(1 + t^2) , cos x= 1/(sqrt(1+t^2)) then show that (dy)/(dx) is independent of t.

If cosx=sqrt(1/(1+t^2)),sin y=(2t)/(1+t^2) then show that (dy)/(dx) is independent of t.

If y=cot^(-1)(sqrt(1+x^2)/x) then (dy)/(dx)=?

If y=sin^(-1)((2sqrt(x^(2)-1))/(x^(2))) , then find (dy)/(dx) .

If y = tan^(-1)sqrt(1+x^2) then find (dy)/(dx) .

If y=sin^(-1)[((5x+12(sqrt(1-x^2)))/13)] then find (dy)/(dx) .

If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)) , then find (dy)/(dx) .

ARIHANT PRAKASHAN-VERY SIMILAR TEST 5-SECTION B
  1. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

    Text Solution

    |

  2. A die is rolled until a 6 is obtained. What is the probability that ...

    Text Solution

    |

  3. Let A=[{:(2,-1),(3,4):}],B=[{:(5,2),(7,4):}]andC=[{:(2,5),(3,8):}]. F...

    Text Solution

    |

  4. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  5. The probability that A hits a target is 1/3 and the probability that B...

    Text Solution

    |

  6. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

    Text Solution

    |

  7. Verify Rolle.s theorem for the function f(x)=x^(2)-3x+2 in the interva...

    Text Solution

    |

  8. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

    Text Solution

    |

  9. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

    Text Solution

    |

  10. Find (dy)/(dx), if y = k tan^(-1) ((y)/(x)).

    Text Solution

    |

  11. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

    Text Solution

    |

  12. Reduce x (dy)/(dx) + y = xy^(3) to linear differential equation.

    Text Solution

    |

  13. Evaluate int [ (1)/( "In" x ) - (1)/(("In" x)^2) ]dx.

    Text Solution

    |

  14. Find the differential equation for the family of curve y= a sin^(-1) x...

    Text Solution

    |

  15. Solve (dy)/(dx) = e^("sin"^(-1) x). (sin^(-1) x)/( sqrt(1-x^(2) ).

    Text Solution

    |

  16. Find the area bounded by the curve y=2 x -x^(2) and the straight line ...

    Text Solution

    |

  17. If the vectors a hat(i) + hat(j) + hat(k),hat(i) + b hat(j) + hat(k) a...

    Text Solution

    |

  18. If a is any vector, then find | hat(i) xx overset(to)(a) |^(2) +|hat(j...

    Text Solution

    |

  19. Find the point of intersection of the line (x-1)/(2) = (y-2)/( -3) = (...

    Text Solution

    |

  20. Answer any three questions (e) Find the foot of perpendicular drawn ...

    Text Solution

    |