Home
Class 12
MATHS
If (sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(...

If `(sin^(-1)x+sin^(-1)w)(sin^(-1)y+sin^(-1)z)=pi^2,` then `D=|x^(N_1)y^(N_3)z^(N_3)w^(N_4)|(N_1,N_2,N_3,N_4 in N)` `

A

has a maximum value of 2

B

has a minimum value of 0

C

16 different D are possible

D

has a minimum value of `-2`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(sin^(-1) x + sin^(-1) w) (sin^(-1) y + sin^(-1) z) = pi^(2)`
`:. Sin^(-1) x + sin^(-1) w = sin^(-1) y + sin^(-1) z = pi`
or `sin^(-1) x + sin^(-1) w = sin^(-1) y + sin^(-1) z = -pi`
`:. x =y = z = w = 1 " or " x = y = z = w = -1`
Hence, the maximum value of `|(x^(N_(1)),y^(N_(2))),(z^(N_(3)),w^(N_(4)))|=|(1,-1),(1,1)|=` minimum value `|(-1,1),(1,1)| = -2
Also, there are 16 diefferent determinants as each place value is either 1 or -1
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

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to

If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n the value of sin^(-1)sin2x is

Evaluate int_(0)^((pi)/2)(sin^(n)xdx)/(sin^(n)x+cos^(n)x)

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

If A=[(1,1,1),(1,1,1),(1,1,1)] , prove that A^(n)=[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))],n in N .

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

If z^(n) = cos"" (n pi)/(3) + isin"" (n pi)/(3), then z_(1), z_(2) …. Z_(6) is

If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= (a) 3 (b) 2 (c) 6 (d) 1

Evaluate the following: 1. sin^(-1)(s i n(2pi)/3) 2. cos^(-1)(c o s(7pi)/6) 3. tan^(-1)(t a n(2pi)/3)

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sq...

    Text Solution

    |

  2. If -1<x<0,t h e ncos^(-1)x is equal to sec^(-1)1/x (b) pi-sin^(-1)sqr...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If sin^(-1)x-cos^(-1)x=(pi)/(6),"then"

    Text Solution

    |

  10. If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 sh...

    Text Solution

    |

  11. If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to...

    Text Solution

    |

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

    Text Solution

    |

  17. If Sn=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+ddotn terms, t...

    Text Solution

    |

  18. Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by

    Text Solution

    |

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

    Text Solution

    |

  20. For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - s...

    Text Solution

    |