Home
Class 12
MATHS
If y=tan^(-1)(cosx/(1+sinx)),then prove ...

If` y=tan^(-1)(cosx/(1+sinx)),`then prove that dy/dx=-1

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

If y=5cosx-3sinx ,then prove that (d^(2)y)/(dx^(2))+y=0

If logsqrt(x^(2)+y^(2))=tan^(-1)((x)/(y)) , then show that (dy)/(dx)=(y-x)/(y+x) .

If y=e^(x)sinx , then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 ,

If y = tan ^(-1)sqrt((1-cosx)/(1+cosx)) , then find (dy)/(dx)

If y=tanx+secx , then prove that (d^(2)y)/(dx^(2))=(cosx)/((1-sinx)^(2))

If x = sin^(-1) ((2t)/( 1 + t^(2) )) and y= tan^(-1) ((2t)/( 1-t^(2) )), t gt 1 prove that (dy)/(dx) = 1 .

Find the derivative of tan^(-1)((cosx)/(1+sinx)) w.r.t. x.

If y=cos^(-1)((2cosx-3sinx)/sqrt13) , then find dy/dx.

If y=tan^(-1)(frac[1+sinx][1-sinx])^(frac[1][2]) and z=log(frac[1+cosx][1-cosx]) , then prove that frac[dy][dx]=frac[-sinx][4]

If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)) , then prove that (dy)/(dx)=(2a^(3))/(x^(4)-a^(4)) .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

    Text Solution

    |

  2. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  3. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1

    Text Solution

    |

  4. Let f(x)={(1/(x+[x]),if xlt0),(-1,if xge0):} Examine the continuity of...

    Text Solution

    |

  5. Show that the function e^x/x^p is strictly increasing for x gt p gt 0.

    Text Solution

    |

  6. Find the equation of tangents and normals to the parabola y^2=4ax at t...

    Text Solution

    |

  7. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  8. Evaluate inte^x((1+sinx)/(1+cosx))dx.

    Text Solution

    |

  9. Evaluate the integral: int(x^2-4)/(x-2)dx

    Text Solution

    |

  10. Solve the following differential equations (x+tany)dy= sin 2y ""dx

    Text Solution

    |

  11. Evaluate int0^7 [x/3]dx

    Text Solution

    |

  12. Prove that the point (1,2,3),(-1,1,0),(2, 1, 3) and (1, 1, 2) are copl...

    Text Solution

    |

  13. If veca and vecb are unit vectors represented by the adjacent sides of...

    Text Solution

    |

  14. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

    Text Solution

    |

  15. Find the angle which a diagonal of a cube makes with one of its edges.

    Text Solution

    |

  16. Find the value of k for which A (1,0,3), B(-1,2,4), C(1,2,1) and D(k,2...

    Text Solution

    |

  17. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

    Text Solution

    |

  18. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

    Text Solution

    |

  19. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

    Text Solution

    |

  20. Find the equation of the tangent and normal to the curve y(x-2)(x-3)-x...

    Text Solution

    |