Home
Class 12
MATHS
Evaluate each of the following: (i)ta...

Evaluate each of the following:
(i)`tan(cos^(-1)(8/(17)))`
(ii) `cot(cos^(-1)(3/5))`
(iii) `cos(tan^(-1)((24)/7))`

Text Solution

AI Generated Solution

To solve the given problems step by step, we will evaluate each expression using the properties of right triangles and the definitions of trigonometric functions. ### (i) Evaluate `tan(cos^(-1)(8/17))` 1. **Let θ = cos^(-1)(8/17)**: This means that cos(θ) = 8/17. 2. **Draw a right triangle**: In this triangle, the adjacent side (base) is 8 and the hypotenuse is 17. ...
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

Evaluate each of the following: cos((cos^(-1)5)/(13))( ii) cos((sin^(-1)8)/(17))( iii) cos((tan^(-1)3)/(4))

Evaluate each of the following: sin((sec^(-1)(17))/(8))( ii) cos ec((cos^(-1)3)/(5))( iii) sec((sin^(-1)(12))/(13))

Evaluate each of the following: sin((sin^(-1)7)/(25)) (ii) sin((cos^(-1)5)/(13))( iii) sin((tan^(-1)(24))/(7))

Evaluate each of the following: sin((sin^(-1)5)/(13)) (ii) sin((cos^(-1)4)/(5))( iii) sin((tan^(-1)(15))/(8))

Evaluate each of the following: tan(csc^(-1)(13)/(5))( ii) tan((sec^(-1)(13))/(12)) (iii) tan((cot^(-1)8)/(15))

Evaluate each of the following: cos^(-1)((cos(13 pi))/(6))( ii) cos^(-1)(cos3)( iii) cos^(-1)(cos4)

Evaluate each of the following: tan((tan^(-1)3)/(4))( ii) tan((sin^(-1)5)/(13))( iii) tan((cos^(-1)8)/(17))

Evaluate each of the following: cos(cot^(-1)(15)/8) (ii) cos(sec^(-1)5/3) (iii) cos("c o s e c"^(-1)(13)/(12))

Evaluate each of the following: sin^(-1)((sin pi)/(3)) (ii) cos^(-1)((cos(2 pi))/(3))( iii) tan^(-1)((tan pi)/(4))

Evaluate each of the following: cos^(-1){cos(-(pi)/(4))}( ii) cos^(-1)((cos(5 pi))/(4)) (iii) cos^(-1)((cos(4 pi))/(3))

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Evaluate each of the following: sin(sin^(-1)(7/(25))) (ii) sin(cos^(...

    Text Solution

    |

  2. Evaluate each of the following: sin(sec^(-1)(17)/8) (ii) "c o s e c...

    Text Solution

    |

  3. Evaluate each of the following: (i)tan(cos^(-1)(8/(17))) (ii) cot(...

    Text Solution

    |

  4. Prove the following results: tan(cos^(-1)4/5+tan^(-1)2/3)=(17)/6 (...

    Text Solution

    |

  5. Prove the following results: tan(sin^(-1)(15)/(13)+cos^(-1)3/5)=(63...

    Text Solution

    |

  6. Solve: cos(sin^(-1)x)=1/6

    Text Solution

    |

  7. Solve: cos{2\ sin^(-1)(-x)}=0

    Text Solution

    |

  8. Evaluate: cos{sin^(-1)(-5/(13))} (ii) cot{sin^(-1)(-7/(25))}

    Text Solution

    |

  9. Evaluate: sec{sin^(-1)(-8/(17))}

    Text Solution

    |

  10. Evaluate: sin{cos^(-1)(-3/5)} (ii) tan{cos^(-1)(-(12)/(13))}

    Text Solution

    |

  11. Evaluate: "c o s e c"{cos^(-1)(-(12)/(13))}

    Text Solution

    |

  12. Evaluate: sin{tan^(-1)(-7/(24))} (ii) cos{cot^(-1)(-5/(12))}

    Text Solution

    |

  13. Evaluate: "c o s e c"{cot^(-1)(-4/3)}

    Text Solution

    |

  14. Prove that: sin^(-1)(-4/5)=tan^(-1)(-4/3)=co^(-1)(-3/5)-pi

    Text Solution

    |

  15. Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0

    Text Solution

    |

  16. Evaluate: cos{sin^(-1)(-7/(25))} (ii) sec{cot^(-1)(-5/(12))} (iii)c...

    Text Solution

    |

  17. Evaluate: cot{sec^(-1)(-(13)/5)}

    Text Solution

    |

  18. Evaluate: (i) tan{cos^(-1)(-7/(25))} (ii) "c o s e c"{cot^(-1)(-(12)...

    Text Solution

    |

  19. Evaluate: sin{sin^(-1)(-(3)/5)+cot^(-1)(-5/(12))}

    Text Solution

    |

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

    Text Solution

    |