Home
Class 12
MATHS
Prove that pi/2 le sin ^(-1) x +2 cos...

Prove that `pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED|37 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    FULL MARKS|Exercise EXERCISE -4.1|7 Videos

  • DISCRETE MATHEMATICS

    FULL MARKS|Exercise Additional Question Solved|20 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    FULL MARKS|Exercise ADDITIONAL PROBLEMS|40 Videos

Similar Questions

Explore conceptually related problems

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

Prove that cos^(2)x + cos^(2)(x + (pi)/(3)) + cos^(2) (x - (pi)/(3)) = (3)/(2)

Prove that pi/6 lt int_0^1(dx) /(sqrt(4-x^2-x^3)) lt pi/(4sqrt(2))

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

The value of sin^(-1) (cos x ) , 0 le x le pi is :

Prove that int_(0)^(pi/4)(sin2xdx)/(sin^(4)x+cos^4 x)=(pi)/(4)

FULL MARKS-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE -4.6
  1. Prove that pi/2 le sin ^(-1) x +2 cos^(-1) x lt (3 pi)/(2)

    Text Solution

    |

  2. The value of sin^(-1) (cos x ) , 0 le x le pi is :

    Text Solution

    |

  3. If sin^(-1)x+sin^(-1)y=(2pi)/(3)",then"cos^(-1)x+cos^(-1)y is equal to

    Text Solution

    |

  4. sin^(-1)""(3)/(5)-cos^(-1)""(12)/(13)+sec^(-1)""(5)/(3)-cosec^(-1)(13)...

    Text Solution

    |

  5. If sin^(-1)x=2sin^(-1)alpha has a solution, then

    Text Solution

    |

  6. sin^(-1)(cosx)=(pi)/(2)-x is valid for

    Text Solution

    |

  7. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) , the value of x^(2017)+y^(...

    Text Solution

    |

  8. If cot^(-1) x = (2pi)/7 for some x in R the value of tan^(-1) x is...

    Text Solution

    |

  9. The domain of the function defined by f(x)=sin^(-1)sqrt(x-1) is

    Text Solution

    |

  10. If x=(1)/(5),"the value of"cos(cos^(-1)x+2sin^(-1)x) is

    Text Solution

    |

  11. tan^(-1)((1)/(4))+tan^(-1)((2)/(9)) is equal to

    Text Solution

    |

  12. If the function f(x)=sin^(-1)(x^(2)-3)" then "x belongs to

    Text Solution

    |

  13. If cot^(-1)2andcot^(-1)3 are two anges of a triangle, then the third a...

    Text Solution

    |

  14. sin^(-1)[tan""(pi)/(4)]-sin^(-1)[sqrt((3)/(x))]=(pi)/(6). Then x is a ...

    Text Solution

    |

  15. sin^(-1)(2cos^(2)x-1)+cos^(-1)(1-2sin^(2)x)=

    Text Solution

    |

  16. If cot^(-1)(sqrt(sinalpha))+tan^(-1)(sqrt(sinalpha))=u,"then"cos2u"is ...

    Text Solution

    |

  17. sin^(-1) ((2x)/(1 + x^(2)))

    Text Solution

    |

  18. The equation tan^(-1)x-cot^(-1)x=tan^(-1)((1)/(sqrt(3))) has

    Text Solution

    |

  19. If cos^(-1)x + cot^(-1) (1/2) = pi/2 then x is equal to

    Text Solution

    |

  20. If sin^(-1)""(x)/(5)+cosec^(-1)""(5)/(4)=(pi)/(2), then the value of x...

    Text Solution

    |

  21. sin(tan^(-1)x)absxlt1 is equal to

    Text Solution

    |