Home
Class 12
MATHS
If y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1...

If `y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))), x in ((pi)/(2), pi)`, then `(dy)/(dx)` at `x=(5pi)/(6)` is :

A

`-1 `

B

`(1)/(2)`

C

`-(1)/(2)`

D

0

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|14 Videos

Similar Questions

Explore conceptually related problems

cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), x in (0,(pi)/(4))

If y="tan"^(-1)((sqrt(1+sinx)+sqrt(1-sinx)))/((sqrt(1+sinx)-sqrt(1-sinx)))," find "(dy)/(dx).

If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] , where 0lt xlt(pi)/(2), then (dy)/(dx) is equal to

Find (dy)/(dx) of y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]

" If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))](0ltxltpi//2)," then "(dy)/(dx)=

If coty=(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))," then "(dy)/(dx)=

(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))=? (x is in IV quadrant)

Show that : cot^(-1) [(sqrt(1 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

JEE MAINS PREVIOUS YEAR-APPLICATION OF DERIVATIVES-All Questions
  1. If y(x) = cot^(-1) ((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-s...

    Text Solution

    |

  2. If p and q are positive real numbers such that p^2+""q^2=""1 , t...

    Text Solution

    |

  3. A value of C for which the conclusion of Mean Value Theorem holds f...

    Text Solution

    |

  4. The function f(x)""=""t a n^(-1)(sinx""+""cosx) is an increasing fu...

    Text Solution

    |

  5. How many real solutions does the equation x^7+""14 x^5+""16 x^3+""3...

    Text Solution

    |

  6. Suppose the cube x^3""p x""+""q has three distinct real roots wh...

    Text Solution

    |

  7. Given P(x)""=""x^4+""a x^3+""c x""+""d such that x""=""0 is the only ...

    Text Solution

    |

  8. The shortest distance between the line yx=1 and the curve x=y^2 is ...

    Text Solution

    |

  9. Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-...

    Text Solution

    |

  10. Let f:""RrarrR be defined by f(x)={(k-2x , if xle-1),( 2x+3, if x gt...

    Text Solution

    |

  11. The equation of the tangent to the curve y""=""x""+4/(x^2) , that is p...

    Text Solution

    |

  12. The shortest distance between line y"-"x""=""1 and curve x""=""y^2 is ...

    Text Solution

    |

  13. A spherical balloon is filled with 4500p cubic meters of helium gas...

    Text Solution

    |

  14. The intercepts on x-axis made by tangents to the curve, y=int0^x|t|...

    Text Solution

    |

  15. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

    Text Solution

    |

  16. A bird is sitting on the top of a vertical pole 20 m high and its e...

    Text Solution

    |

  17. The normal to the curve, x^2+""2x y-3y^2=""0,""a t""(1,""1) : (1) ...

    Text Solution

    |

  18. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

    Text Solution

    |

  19. A wire of length 2 units is cut into two parts which are bent respe...

    Text Solution

    |

  20. The radius of a circle, having minimum area, which touches the curve y...

    Text Solution

    |

  21. Twenty metres of wire is available for fencing off a flower-bed in ...

    Text Solution

    |