Home
Class 12
MATHS
sin(pi/3-sin^(-1)(-1/2))is equal to(A) 1...

`sin(pi/3-sin^(-1)(-1/2))`is equal to(A) `1/2` (B) `1/3` (C) `1/4` (D) 1

A

`(1)/(2)`

B

`(1)/(3)`

C

`(1)/(4)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
`sin[(pi)/(3)-sin^(-1)""(-(1)/(2))]`
`=sin[(pi)/(3)+sin^(-1)""(1)/(2)]`
`=sin[(pi)/(3)+sin^(-1)""(sin""(pi)/(6))]`
`=sin[(pi)/(3)+ (pi)/(6)]=sin""(pi)/(2)=1`
Promotional Banner

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|8 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exericse 2.1|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to (A) 0,1/2 (B) 1,1/2 (C) 0 (D) 1/2

sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to (A) 0,1/2 (B) 1,1/2 (C) 0 (D) 1/2

tan^(-1)sqrt(3)-sec^(-1)(-2) is equal to(A) pi (B) -pi/3 (C) pi/3 (D) (2pi)/3

tan^(-1)sqrt(3)-sec^(-1)(-2) is equal to(a) pi (B) -pi/3 (C) pi/3 (D) (2pi)/3

sin(tan^(-1)99 + cot^(-1)99) is equal to a) 0 b) -1 c) 1/2 d) 1

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

tan^(-1)((-1+sin1)/(cos1)) equals (A) 0 (B) 1-pi/2 (C) pi/2-1 (D) 1/2-pi/4

The value of cos^(-1)sqrt(2/3)-cos^(-1)((sqrt(6)+1)/(2sqrt(3))) is equal to (A) pi/3 (B) pi/4 (C) pi/2 (D) pi/6

If sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2, then x is equal to 7/(13) (b) 4/3 (c) 13 (d) (13)/7

If sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2, then x is equal to 7/(13) (b) 4/3 (c) 13 (d) (13)/7

NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2.2
  1. Prove that: 3cos^(-1)x=cos^(-1)(4x^3-3x), x in [1/2,1]

    Text Solution

    |

  2. Prove that : tan^(-1)2/(11)+tan^(-1)7/(24)=tan^(-1)1/2

    Text Solution

    |

  3. Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

    Text Solution

    |

  4. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

    Text Solution

    |

  5. tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

    Text Solution

    |

  6. Express each of the following in the simplest form: tan^(-1){sqrt((...

    Text Solution

    |

  7. tan^(-1)((cosx-sinx)/(cosx+sinx))=pi/4-x

    Text Solution

    |

  8. tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

    Text Solution

    |

  9. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

    Text Solution

    |

  10. For the principal values, evaluate each of the following: tan^(-1){2co...

    Text Solution

    |

  11. Find the value of: cot(tan^(-1)a+cot^(-1)a)

    Text Solution

    |

  12. Find the value of: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)...

    Text Solution

    |

  13. If sin(sin^(-1)1/5+cos^(-1)x)=1, then find the value of xdot

    Text Solution

    |

  14. tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4. find X

    Text Solution

    |

  15. Find the value of sin^(-1)(sin((2pi)/3))

    Text Solution

    |

  16. Find the value of tan^(-1)(tan((3pi)/4))

    Text Solution

    |

  17. Find the value of tan(sin^(-1)3/5+cot^(-1)3/2)

    Text Solution

    |

  18. cos^(-1)(cos(7pi)/6)is equal to(a) (7pi)/6 (B) (5pi)/6 (C) pi/3 (D) pi...

    Text Solution

    |

  19. sin(pi/3-sin^(-1)(-1/2))is equal to(A) 1/2 (B) 1/3 (C) 1/4 (D) 1

    Text Solution

    |

  20. tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))is equal to (A) pi (B) -pi/2 (C) 0 ...

    Text Solution

    |