Home
Class 12
MATHS
If sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"...

If `sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot`

Text Solution

Verified by Experts

Let `t = tan theta`
Then, `sinx = (2tan theta)/(1+tan^2theta)`
As, `(2tan theta)/(1+tan^2theta) = sin2theta`,
`=> sin x = sin2theta`
`=> x= 2npi+2theta`
`=>dx/ (d theta) = 2 `
Now, `tan y = (2tan theta)/(1-tan^2theta)`
As, `(2tan theta)/(1- tan^2theta) = tan2theta`,
...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

If sinx=(2t)/(1+t^(2)),tany=(2t)/(1-t^(2)),"find "dy/dx

If sin x=(2t)/(1+t^(2)),tan y=(2t)/(1-t^(2)), find (dy)/(dx)

sinx = (2t)/(1+t^(2)), tan y = (2t)/(1-t^(2))

If x=(2t)/(1+t^(2)),y=(1-t^(2))/(1+t^(2))," then "(dy)/(dx)=

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)) , then (dy)/(dx) is equal to

If x=a((1+t^(2))/(1-t^(2))) and y=(2t)/(1-t^(2)), find (dy)/(dx)

If x=a((1+t^(2))/(1-t^(2))) and y=(2t)/(1-t^(2)), find (dy)/(dx)

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If x=(1+logt)/(t^2),y=(3+2logt)/t ,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  2. If x=3sint-sin3t ,y=3cos t-cos3t ,"f i n d"(dy)/(dx)"a t"t=pi/3dot

    Text Solution

    |

  3. If sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot

    Text Solution

    |

  4. Differentiate tan^(-1)((cosx)/(1+sinx)) with respect to sec^(-1)...

    Text Solution

    |

  5. If cosy=xcos(a+y), with cosa!=+-1, prove that (dy)/(dx)=(cos^2(a+y)...

    Text Solution

    |

  6. If f(x)=(log)(x^2)(logx), then f^(prime)(x) at x=e is 0 (b) 1 (c) 1...

    Text Solution

    |

  7. The derivative of the function cot^(-1){(cos2"x")^(1/2)}a tx=pi/6 is (...

    Text Solution

    |

  8. If f(x),g(x)and h(x) are three polynomials of degree 2, then prove tha...

    Text Solution

    |

  9. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...

    Text Solution

    |

  10. If 3sin(x y)+4cos(x y)=5 then dy/dx=

    Text Solution

    |

  11. If f(x)=((x^l)/(x^m))^(l+m)((x^m)/(x^n))^(m+n)((x^n)/(x^l))^(n+l), the...

    Text Solution

    |

  12. d/(dx){tan^(-1)((cosx)/(1+sinx))}e q u a l 1/2 (b) x (c) (1-x^2)/(1...

    Text Solution

    |

  13. Ify=sqrt(sinx+y ,) then (dy)/(dx)= (sinx)/(2y-1) (b) (sinx)/(1-2y) ...

    Text Solution

    |

  14. If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)...

    Text Solution

    |

  15. If sin^(-1)((x^2-y^2)/(x^2+y^2))=logat h e n(dy)/(dx)is equal to (x^...

    Text Solution

    |

  16. If (1+x)^n=c0+C1x+C2x^2++Cn x^n ,using derivative prove that C1+2...

    Text Solution

    |

  17. Differentiate the following function with respect to x, "tan"(x^0+...

    Text Solution

    |

  18. If y={x+sqrt(x^2+a^2)}^n , then prove that (dy)/(dx)=(n y)/(sqrt((x^2...

    Text Solution

    |

  19. If y=(xsin^(-1)x)/(sqrt(1-x^2))+logsqrt(1-x^2) , then prove that (dy)...

    Text Solution

    |

  20. Differentiate the following functions with respect to x : log(secx+ta...

    Text Solution

    |