Home
Class 12
MATHS
If x in [-1,0], then find the value of c...

If `x in [-1,0],` then find the value of `cos^(-1)(2x^2-1)-2sin^(-1)x`

Text Solution

Verified by Experts

The correct Answer is:
`pi`
`cos^(-1) (2x^(2) -1) = 2pi - 2 cos^(-1) x " " ("as " x lt 0)`
`rArr cos^(-1) (2x^(2) -1) -2 sin^(-1) x = 2pi - 2 cos^(-1) x - 2sin^(-1) x`
`= 2pi - 2 (cos^(-1) x + sin^(-1) x)`
`= 2pi - 2 (pi)/(2) = pi`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

Find the value of sin^(-1)x+sin^(-1)1/x+cos^(-1)x+cos^(-1)1/xdot

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

If sinx+sin^2x=1 , then find the value of cos^(12)x +3cos^(10)x + 3 cos^8x + cos^6x-1

If (x -1) (x^(2) + 1) gt 0 , then find the value of sin((1)/(2) tan^(-1).(2x)/(1 - x^(2)) - tan^(-1) x)

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

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

If (x^(+(1)/(2)) + x^(-(1)/(2)))^(2) = (9)/(2) , then find the value of (x^((1)/(2))-x^(-(1)/(2))) for x gt 1 .

If cos (2 sin^(-1) x) = (1)/(9) , then find the value of x

If sin^(-1)x_i in [0,1]AAi=1,2,3, .28 then find the maximum value of sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+ sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)++sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)

If sin^(-1)((1)/(2))=tan^(-1)x, then find the value of x.

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the value of x which satisfy equation 2 tan^(-1) 2x = sin^(-1).(4...

    Text Solution

    |

  2. If x in (0, 1), then find the value of tan^(-1) ((1 -x^(2))/(2x)) + co...

    Text Solution

    |

  3. If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

    Text Solution

    |

  4. sin(2sin^(-1) 0.8)=

    Text Solution

    |

  5. cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) is equal to

    Text Solution

    |

  6. The value of sin^(-1)("cot"(sin^(-1)((2-sqrt(3))/4+cos^(-1)(sqrt(12))...

    Text Solution

    |

  7. If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) ...

    Text Solution

    |

  8. If cosec^(-1) (cosec x) and cosec (cosec^(-1) x) are equal function th...

    Text Solution

    |

  9. sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is equal to (a)5 (b) 13 (c) 15...

    Text Solution

    |

  10. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is...

    Text Solution

    |

  11. For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real soluti...

    Text Solution

    |

  12. The number of real solution of the equation tan^(-1) sqrt(x^(2) - 3x +...

    Text Solution

    |

  13. If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then ...

    Text Solution

    |

  14. The number of real solution of the equation sqrt(1+cos2x)=sqrt2 sin^(-...

    Text Solution

    |

  15. Find the set of value of x for which the equation cos^(-1) x + cos^(-1...

    Text Solution

    |

  16. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (pi/4,(3pi)/4) (b) [pi...

    Text Solution

    |

  17. The value of lim(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equ...

    Text Solution

    |

  18. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  19. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

    Text Solution

    |

  20. The number of integral values of k for which the equation sin^(-1)x+ta...

    Text Solution

    |