Home
Class 12
MATHS
If n=pi/(4alpha), then tan alpha tan 2al...

If `n=pi/(4alpha),` then `tan alpha tan 2alpha tan 3 alpha ... tan(2n-1)alpha` is equal to (a) 1 (b) 1/2 (c) 2 (d) 1/3

A

1

B

`1//2`

C

2

D

`1//3`

Text Solution

Verified by Experts

The correct Answer is:
A
`alpha+2alpha+4alpha=7alpha=(pi)/(2)`
`therefore tan alpha. Tan 2 alpha+tan 2 alpha. Tan 4 alpha+tan alpha. Tan 4 alpha=1`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Exercise (Multiple Correct Answer Type)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Exercise (Linked Comprehension Type)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Concept App. 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If 4nalpha=pi , then cotalpha cot2alpha cot3alpha.... cot(2n-1)alpha is equal to

If 4nalpha=pi , then the numerical value of tanalpha, tan2alpha,tan3alpha.....tan(2n-1)alpha is equal to

If 2n alpha= pi/2, then show that tan alpha tan 2 alpha tan 3 alpha.... Tan (2n-2) alpha tan (2n-1) alpha=1

If alpha=pi/(14), then the value of (tanalphatan2alpha+tan2alphatan4alpha+tan4alphatanalpha) is 1 (b) 1//2 (c) 2 (d) 1//3

Prove that, tan 8alpha - tan 5 alpha - tan 3 alpha = tan 8alpha tan 5 alpha tan 3 alpha

int (tan x - tan alpha)/(tan x+tan alpha)dx

If (1+tanalpha)(1+tan4alpha)=2,alpha in (0,pi/(16)), then alpha is equal to

If tan alpha + cot alpha=2 , then the value of tan^(13) alpha +cot^(13) alpha is

Show that tan8alpha-tan5alpha-tan3alpha=tan8alphatan5alphatan3alpha

CENGAGE PUBLICATION-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. If costheta1 2costheta2, then tan(theta(1-theta2))/2tan(theta1+theta2)...

    Text Solution

    |

  2. Let alpha and beta be such that pi<alpha-beta<3pi, If sinalpha+sinbeta...

    Text Solution

    |

  3. If n=pi/(4alpha), then tan alpha tan 2alpha tan 3 alpha ... tan(2n-1)a...

    Text Solution

    |

  4. (sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos ...

    Text Solution

    |

  5. If x , y , z are in A.P., then (sinx-sinz)/(cosz-cosx) is equal to ...

    Text Solution

    |

  6. If cosx/a=cos(x+theta)/b=cos(x+2theta)/c=cos(x+3theta)/d then (a+c)/(b...

    Text Solution

    |

  7. If cosalpha+cosbeta=0=sinalpha+sinbeta, then cos2alpha+cos2beta is equ...

    Text Solution

    |

  8. Value of (3+cot80^0cot20^0)/(cot80^0+cot20^0) is equal to cot20^0 (b)...

    Text Solution

    |

  9. If tanalpha is equal to the integral solution of the inequality 4x^2-1...

    Text Solution

    |

  10. Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to f(n+3) (...

    Text Solution

    |

  11. If sintheta1sintheta2-costheta1costheta2+1=0, then the value of tan((t...

    Text Solution

    |

  12. (sqrt(2)-sinalpha)/(sinalphapi-cosalphapi) is equal to sec(alpha/2-pi/...

    Text Solution

    |

  13. If x(1) and x(2) are two distind roots of the equation a cos x+b sinx=...

    Text Solution

    |

  14. If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ...

    Text Solution

    |

  15. If (tan(alpha+beta+gamma))/("tan"(alpha-beta-gamma))=(tangamma)/(tanbe...

    Text Solution

    |

  16. If sintheta(1)-sintheta(2)=a and cos theta(1)+costheta(2)=b, then

    Text Solution

    |

  17. The value of expression (2(sin1^0+sin2^0+sin3^0++sin89^0)/(2(cos1^0+co...

    Text Solution

    |

  18. If A,B,C, are the angles of a triangle such that cotA/2=3tanC/2, then ...

    Text Solution

    |

  19. If 2sec 2theta=tan phi+cotphi, then one of the values of theta+phi is

    Text Solution

    |

  20. The roots of the equation 4x^2-2sqrt5 x +1=0 are .

    Text Solution

    |