Home
Class 11
MATHS
Evaluate {sin(2tan^-1 (1/3))} + {cos(t...

Evaluate
`{sin(2tan^-1 (1/3))} + {cos(tan^-1(2sqrt2))}`
where {.} denotes the fractional part function

A

44260

B

14/15

C

16/15

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos
  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of y =(1)/({x}) , where {*} denotes the fractional part function.

The function 'g' defined by g(x)= sin(sin^(-1)sqrt({x}))+cos(sin^(-1)sqrt({x}))-1 (where {x} denotes the functional part function) is (1) an even function (2) a periodic function (3) an odd function (4) neither even nor odd

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) (cos^2(1-cos^2(1-cos^2.......cos^2(x)......)))/(sin[pi((sqrt(x+4) - 2)/x) ]

Number of solutions of the equation [2x] - 3{2x} = 1 is (where [/] and {.} denote greatest integer and fractional part function respectively)

Solve for x : If [ sin^-1(cos^-1(sin^-1(tan^-1x)))]=1 , where [cdot] denotes the greatest integer function.

Find the value of int_(-1)^(1)[x^(2)+{x}]dx , where [.] and {.} denote the greatest function and fractional parts of x , respectiely.

underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the greatest integer function)

Find the value of sin cot^-1 cos (tan^-1(2))

The period of function 2^({x}) +sin pi x+3^({x//2})+cos pi x (where {x} denotes the fractional part of x) is

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. The value of x between 0 and 2 pi which satisfy the equation sinxsqrt(...

    Text Solution

    |

  2. The solution set of inequality log(1/2) sin^-1 x gt log(1/2) cos^-1 x

    Text Solution

    |

  3. Evaluate {sin(2tan^-1 (1/3))} + {cos(tan^-1(2sqrt2))} where {.} de...

    Text Solution

    |

  4. The number of real solutions of sin e^x cdot cos e^x = 2^(x -2) + 2^(-...

    Text Solution

    |

  5. If theta in [0 , 5pi] and r in R such that 2 sin theta = r^4 - 2r^2 + ...

    Text Solution

    |

  6. The integer k for which the equation 7cosx+5sinx=2k+1 has a solution i...

    Text Solution

    |

  7. If 1/6 sin x , cos x , tan x are in G.P. then x is equal to

    Text Solution

    |

  8. The equation sin x = x^2 + x + 1 has

    Text Solution

    |

  9. In a triangle ABC, angle A is greater than angle B. If the measures of...

    Text Solution

    |

  10. If k1 le sin^-1 x + cos^-1 x + tan^-1 x le k2 then

    Text Solution

    |

  11. If sin^-1(x - x^2/2 + x^3/4 - ..... infty) + cos^-1 (x^2 - x^4/2 + x^6...

    Text Solution

    |

  12. cot^-1 (9/2) + cot^-1 (25/2) + cot^-1 (49/2) + ........ to n terms is ...

    Text Solution

    |

  13. The interval on which cos^-1 x gt sin^-1 x gt tan^-1 x is

    Text Solution

    |

  14. If (cos^2 x + 1/(cos^2 x)) (1 + tan^2 2y)(3 + sin 3z) = 4 ,then

    Text Solution

    |

  15. 2 sin^2(pi/2 cos^2 x) = 1 - cos(pi sin 2x). if

    Text Solution

    |

  16. sqrt(cos 2x) + sqrt(1 + sin 2x) = 2sqrt(sin x + cos x) if

    Text Solution

    |

  17. If tan^-1 y = 4 tan^-1 x , then y is infinite , if

    Text Solution

    |

  18. The solution of the equation sin[2cos^-1{cot(2tan^-1x)}] = 0 are

    Text Solution

    |

  19. If the numerical value of tan{cos^-1(4/5)+tan^-1(2/3)} is a/b , then

    Text Solution

    |

  20. If x gt 0 , then tan^-1 x =

    Text Solution

    |