Home
Class 12
MATHS
यदि tantheta+tan(theta+pi/3)+tan(theta-p...

यदि `tantheta+tan(theta+pi/3)+tan(theta-pi/3)=ktan3theta` तब `k=`

A

`1`

B

`3`

C

`1/3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`tan theta+tan(theta+(pi)/(3))+tan(theta-(pi)/(3))`
`=tan theta+(tantheta+sqrt3)/(1-sqrt3tantheta)+(tantheta-sqrt3)/(1+sqrt3tantheta)`
`tan theta(1-3tan^(2)theta)+(tan theta+sqrt3)(1+sqrt3tantheta)`
` =(+(tantheta-sqrt3)(1-sqrt3tantheta))/(1-3tan^(2)theta)`
`=3((3tantheta-tan^(3)theta)/(1-3tan^(2)theta))=3tan3 theta`
`therefore k=3.`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Exercise|190 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

tan theta+tan(theta+(pi)/(3))+tan(theta-(pi)/(3))=k tan36 then k is equal to

tantheta+tan2theta=tan3theta

tan theta tan((pi)/(3)+theta)tan((pi)/(3)-theta)=tan3 theta

Solve: tan^(3)theta-3tantheta=0

tantheta+tan(pi/3+theta)+tan((2pi)/(3)+theta)=3

tan(pi/4+theta)+tan(pi/4-theta)=4

OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. The Minimum value of 27^cosx +81^sinx is equal to

    Text Solution

    |

  2. The value of tan alpha +2tan(2alpha)+4tan(4alpha)+...+2^(n-1)tan(2^(n...

    Text Solution

    |

  3. यदि tantheta+tan(theta+pi/3)+tan(theta-pi/3)=ktan3theta तब k=

    Text Solution

    |

  4. For 0ltxlt(pi)/(6), all the values of tan^(2)3x cos^(2)x-4tan3xsin2x+1...

    Text Solution

    |

  5. In a cyclic quadrilateral ABCD, the value of 2+sum cos A soc B, is

    Text Solution

    |

  6. If x+y+z=pi, tan x tanz=2 and tanytanz=18,then tan^(2)z=

    Text Solution

    |

  7. Biggest among (sin1+cos1),(sqrt(sin1))+sqrt(cos1)),sqrt(1+sin2)and 1...

    Text Solution

    |

  8. In a DeltaABC, if tanA+2tanB=0, then which one is correct?

    Text Solution

    |

  9. The maximum value of 1+sin(pi/4+theta)+2cos(pi/4-theta) for real value...

    Text Solution

    |

  10. If y =4sin^(2)theta-cos2theta,then y lies in the interval

    Text Solution

    |

  11. If y=cos^2theta+sin^4theta then for all real values of theta

    Text Solution

    |

  12. The ratio of the greatest value of 2-cos x+s in^2x to its least value ...

    Text Solution

    |

  13. The least value of [cos^2 theta-6 sin theta. cos theta+3 sin^2 theta +...

    Text Solution

    |

  14. If y=tan^(2)theta+sectheta, thetane(2n+1)pi//2,then

    Text Solution

    |

  15. Two parallel chords of a circle, which are on the same side of centre,...

    Text Solution

    |

  16. If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then

    Text Solution

    |

  17. If sinx+cosx=1/5,0lexlepi, then tan x is equal to

    Text Solution

    |

  18. For for A=133^(@),2cos""A/2is equal to

    Text Solution

    |

  19. A and B are positive acute angles satisfying the equations 3cos^(2)A+2...

    Text Solution

    |

  20. The expression (cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx) is equ...

    Text Solution

    |