Home
Class 12
MATHS
if (1+tanalpha)(1+tan4alpha) =2 where al...

if (1+tan`alpha`)(1+tan4`alpha`) =2 where `alpha` `in` (0 , `pi/16`) then `alpha ` equal to

A

`(pi)/(20)`

B

`(pi)/(30)`

C

`(pi)/(40)`

D

`(pi)/(60)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1+tanA)(1+tanB)=2`
`rArr tan A+tan B=1-tan A tan B`
`rARr tan(A+B)=1,i.e, A+B=(pi)/(4)`
or `alpha+4alpha=(pi)/(4)` i.e. `alpha=(pi)/(20)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

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

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If (1+tan alpha)(1+tan4 alpha)=2,alpha in(0,(pi)/(16)) then alpha is equal to (a) (pi)/(20) (b) (pi)/(30) (c) (pi)/(40) (d) (pi)/(60)

1+tan alpha*tan((alpha)/(2))

If z=1+i tan alpha where pi lt alpha lt(3pi)/(2), then what is |z| equal to ?

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to

If tan(alpha+beta)=2andtan (alpha-beta)=1 , then tan(2alpha) is equal to

If 0 lt alpha lt (pi)/(16) and (1+tan alpha)(1+tan4alpha)=2 , then the value of alpha is equal to

If tan (alpha + beta) = 2 and tan (alpha - beta) = 1, then tan (2 alpha ) is equal to:

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. The minimum vertical distance between the graphs of y=2+s in xa n dy=c...

    Text Solution

    |

  2. If tan^2(pi-A)/4+tan^2(pi-B)/4+tan^2(pi-C)/4=1 , then A B C is equila...

    Text Solution

    |

  3. if (1+tanalpha)(1+tan4alpha) =2 where alpha in (0 , pi/16) then alpha...

    Text Solution

    |

  4. If cos28^0+sin28^0=k^3, t h e ncos17^0 is equal to (k^3)/(sqrt(2)) (b...

    Text Solution

    |

  5. Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the va...

    Text Solution

    |

  6. If y = (1 + tan A) (1 - tan B), where A -B=pi/4 then (y+ 1)^(y + 1) is...

    Text Solution

    |

  7. If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2, where x,y in (0,pi/2), then th...

    Text Solution

    |

  8. If cot^2x=cot(x-y)(x-z),t h e ncot2x is equal to (w h e r ex!=pi/4) ....

    Text Solution

    |

  9. In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB si...

    Text Solution

    |

  10. find the value of sin 27^(@)-cos27^(@)?

    Text Solution

    |

  11. If costheta1 2costheta2, then tan(theta(1-theta2))/2tan(theta1+theta2)...

    Text Solution

    |

  12. Let alpha, beta be such that it pi < alpha - beta <3 pi. if sin alph...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If cos alpha+cos beta=0=sin alpha+sinbeta, then cos2alpha+cos 2beta=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |