Home
Class 12
MATHS
If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin...

If `tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n` the value of `sin^(-1)2x` is `6-2pi` (b) `2pi-6` `pi-3` (d) `3-pi`

A

`6 - 2pi`

B

`2pi - 6`

C

`pi - 3`

D

`3 -pi`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`tan^(-1) (x^(2) + 3 |x| -4) + cot^(-1) (4 pi + sin^(-1) sin 14) = (pi)/(2)`
`rArr tan^(-1) (x^(2) + 3 |x| -4) + cot^(-1) (4pi + 14 - 4pi) = (pi)/(2)`
`rArr x^(2) + 3 |x| -4 = 14`
`rArr x^(2) + 6 |x| -3 |x| -18 = 0`
`rArr x = +- 3`
So, `sin^(-1) sin 2x = sin^(-1) sin 6 - 2pi`
or `sin^(-1) sin (-6) = 2pi - 6`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|16 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|80 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4 pi+sin^(-1)sin14)=(pi)/(2), then the value of sin^(-1)sin2x is (a)6-2 pi( b) 2 pi-6( c) pi-3 (d) 3-pi

If tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin14)=(pi)/(2) , then the value of sin^(-1)(sin2x) can be equal to

If tan x=(-3)/(4) and (3 pi)/(2)

If sin^(-1)x+sin^(-1)y=(2 pi)/(3) ,then the value of cos^(-1)x+cos^(-1)y is (A) (2 pi)/(3) (B) (pi)/(3) (C) (pi)/(2) (D) pi

sin^(-1)((-1)/2) (a) pi/3 (b) -pi/3 (c) pi/6 (d) -pi/6

If sin theta=(1)/(2) and cos theta=-(sqrt(3))/(2), then the general value of theta is (n in Z)*( a) 2n pi+(5 pi)/(6) (b) 2n pi+(pi)/(6)2n pi+(7 pi)/(6)( d) 2n pi+(pi)/(4)

If y=tan^(-1)x+tan^(-1)(1/x)+sec^(-1)x , then y lies in the interval (a) [pi/2,pi)uu[pi,(3pi)/2) (b) [pi/2,(3pi)/2] (c)(0,pi) (d) [0,pi/2)uu[pi/2,pi)

If sin^(-1)(tan pi//4)-sin^(-1)(sqrt(3//x))-pi//6=0 , then x is a root of the equation

If lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,where theta in (-pi,pi], then the value of theta is (a)+-pi/4 (b) +-pi/3 (c) +-pi/6 (d) +-pi/2

If sin^(-1)(tan(pi)/4)-sin^(-1)(sqrt(3/y))-(pi)/6=0 and x^(2)=y then x is equal to

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Multiple)
  1. Which of the following quantities is/are positive ?

    Text Solution

    |

  2. If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sq...

    Text Solution

    |

  3. If -1 lt x lt 0, then cos^(-1) x is equal to

    Text Solution

    |

  4. If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^2, then D=|x^(N1)y^(N...

    Text Solution

    |

  5. Indicate the relation which can hold in their respective domain for ...

    Text Solution

    |

  6. If cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6, where x y<0 then the possible v...

    Text Solution

    |

  7. If z = sec^(-1) (x + 1/x) + sec^(-1) (y + 1/y), where xy< 0, then the ...

    Text Solution

    |

  8. The value of k(k >0) such that the length of the longest interval in w...

    Text Solution

    |

  9. Which of the following pairs of function/functions has same graph? y=...

    Text Solution

    |

  10. If sin^(-1) x + sin^(-1) y = (pi)/(2) and sin 2x = cos 2y, then

    Text Solution

    |

  11. If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal ...

    Text Solution

    |

  12. If sin^(-1)(a-a^2/3+a^3/9-...)+cos^(-1)(1+b+b^2+...)=pi/2 then find a ...

    Text Solution

    |

  13. If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)s in 14)=pi/2, t h e n th...

    Text Solution

    |

  14. If 2tan^(-1)x+sin^(-1)((2x)/(1+x^2) ) is independent of x then :

    Text Solution

    |

  15. If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2))...

    Text Solution

    |

  16. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to...

    Text Solution

    |

  17. Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/...

    Text Solution

    |

  18. If Sn=cot^-1(3)+cot^-1(7)+cot^-1(13)+cot^-1(21)+....., n terms, then

    Text Solution

    |

  19. Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by exactly one value ...

    Text Solution

    |

  20. To the equation 2^2pi//cos^((-1)x)-(a+1/2)2^pi//cos^((-1)x)-a^2=0 has ...

    Text Solution

    |