Home
Class 12
MATHS
Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-...

Consider `f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot` A normal to `y=f(x)` at `x=pi/6` also passes through the point: (1) (0, 0) (2) `(0,(2pi)/3)` (3) `(pi/6,0)` (4) `(pi/4,0)`

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

If f(x) = tan^(-1)(sqrt((1+sinx)/(1-sinx))), 0 lt x lt pi/2 , then f'(pi/6) is

If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2) then f' ((pi)/(6)) =?

int_(0)^(pi)(x sinx)/((1+sinx))dx=pi((pi)/(2)-1)

If 0

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

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 :

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

f(x)=[x tan^(-1)x+sec^(-1)((1)/(x)),x in(-1,1)-{0} and (pi)/(2), if x=0, then f'(0) is

tan^(-1)x+tan^(-1)(1)/(x)={[(pi)/(2), if x>0-(pi)/(2), if x<0

JEE MAINS PREVIOUS YEAR-APPLICATION OF DERIVATIVES-All Questions
  1. A value of C for which the conclusion of Mean Value Theorem holds f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve ...

    Text Solution

    |