Home
Class 12
MATHS
Show that sin^(-1)""(3)/(5)-sin^(-1)""(8...

Show that `sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)`

Text Solution

Verified by Experts

Let `sin^(-1)3/5=x` and `sin^(-1)8/17=y`,Then,
`sinx=3/5` and `siny=8/17`.
`therefore cosx=sqrt(1-sin^(2)x)=sqrt(1-9/25)=sqrt(16/25)=4/5`
and `cosy=sqrt(1-sin^(2)y)=sqrt(1-64/25)=sqrt(225/289)=15/17`.
`therefore cos(x-y)=cosxcosy+sinxsiny`
`=(4/5 xx 15/17) +(3/5 xx 8/17) = (12/17+24/85)=84/85`
`rArr x-y=cos^(-1)(84/85) rArr sin^(-1)3/5-sin^(-1)8/17=cos^(-1)84/85`.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4A|4 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4B|22 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

Show that : sin^(-1) (3/5) + sin^(-1) (8/17) = cos^(-1) (36/85) .

Prove that sin^(-1)((8)/(17))+sin^(-1)((3)/(5))=cos^(-1)((36)/(85))

Prove that sin^(-1)(3/5)+cos^(-1)(15/17)=cos^(-1)(36/85)

sin^(-1)((8)/(17))+sin^(-1)((3)/(5))=

Prove each of the following sin^(-1)((3)/(5))+sin^(-1)((8)/(17))=sin^(-1)((77)/(85))

Prove each of the following sin^(-1)((3)/(5))+sin^(-1)((8)/(17))=sin^(-1)((77)/(85))

Prove that sin^(-1) . 3/5 - sin ^(-1) . 8/17 = cos^(-1) . 84/85

Show that : sin^(-1)(8/(17))+sin^(-1)(3/5)=sin^(-1)(77/85)

Show that : 2 sin^(-1) (3/5)-tan^(-1) (17/31) = pi/4

RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Objective Questons
  1. Show that sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)

    Text Solution

    |

  2. Find the principal value of: cos^(-1)((sqrt(3))/2)

    Text Solution

    |

  3. Find the principal value of the following: (i) cosec^(-1)(2) (ii) ta...

    Text Solution

    |

  4. Find the principal value of: cos^(-1)(-1/(sqrt(2)))

    Text Solution

    |

  5. Find the principal value of: sin^(-1)(-1/2)

    Text Solution

    |

  6. The principal value of cos^(-1)(-1/2) is

    Text Solution

    |

  7. The principal value of tan^-1(-sqrt3) is

    Text Solution

    |

  8. The principal value of cot^(-1)(-1) is

    Text Solution

    |

  9. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

    Text Solution

    |

  10. The principal value of "cosec"^(-1)(-sqrt(2)) is

    Text Solution

    |

  11. Find the principal values of each of the following: cot^(-1)(-sqrt(...

    Text Solution

    |

  12. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

    Text Solution

    |

  13. The value of cos^(-1)(cos(14pi/6)) is

    Text Solution

    |

  14. The value of tan^(-1)(tan(8*pi/6)) is

    Text Solution

    |

  15. Find the value of : cot^(-1), (5pi/4)

    Text Solution

    |

  16. The value of sec^(-1)(sec(8pi)/5) is

    Text Solution

    |

  17. The value of "cosec"^(-1)("cosec"(4pi)/3) is

    Text Solution

    |

  18. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

    Text Solution

    |

  19. pi/3-sin^(-1)(-1/2)=?

    Text Solution

    |

  20. The value of sin(sin^(-1)(1/2)+cos^(-1)(1/2))=?

    Text Solution

    |

  21. If x ne 0 then cos(tan^(-1)+cot^(-1)x)=?

    Text Solution

    |