Home
Class 12
MATHS
tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 7...

`tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1`

A

1

B

`1//2`

C

`1//4`

D

`1//8`

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`tan6^(@) tan 42^(@) tan66^(@)tan78^(@)`
`=tan 6^(@)tan(60^(@)-18^(@))tan(60^(@)+6^(@))tan(60^(@)+18^(@))`
`=([tan6^(@)tan(60^(@)+6^(@))tan18^(@)tan(60^(@)-18^(@))tan(60^(@)+18^(@))])/(tan18^(@))`
`=(tan6^(@)tan(60^(@)+6^(@))tan(3xx18^(@)))/(tan18^(@))`
`=(tan6^(@)tan(60^(@)-6^(@))tan(60^(@)+6^(@)))/(tan18^(@))`
`=(tan18^(@))/(tan18^(@))=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

Show that tan 48^(@) tan 16^(@)tan 42^(@) tan 74^(@) =1

Prove that, tan 1^(@) tan 2^(@) tan 3^(@).....tan 87^(@) tan 88^(@) tan 89^(@) = 1 .

Prove that, tan 35^(@) + tan 10^(@) + tan35^(@) tan 10^(@) = 1

The value of (tan 9^(@)-tan 27^(@)-tan 63^(@)+tan 81^(@)) is-

Show that, tan 181^(@) tan182^(@) tan 183^(@).....tan 267^(@) tan 268^(@) tan 269^(@) = 1 .

The value of tan 31^(@) tan 32^(@)tan 33^(@)…tan 59^(@) is-

Prove that tan4^(@)tan43^(@)tan47^(@)tan86^(@)=1 .

If tan 17^(@) = x , find the value of (tan 163^@ - tan 107^@)/(1 + tan 163^@ tan 107^@) .

(2 tan 30^(@))/( 1-tan ^(2) 30^(@)) =

CENGAGE PUBLICATION-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. Given that a , b , c , are the side of a A B C which is right angled ...

    Text Solution

    |

  2. If theta=3alpha and sin theta=(a)/(sqrt(a^(2)+b^(2)) , the value of th...

    Text Solution

    |

  3. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

    Text Solution

    |

  4. In triangle A B C , if angle is 90^0 and the area of triangle is 30 sq...

    Text Solution

    |

  5. If sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A...

    Text Solution

    |

  6. In a right angled triangle the hypotenuse is 2sqrt(2) times the perpen...

    Text Solution

    |

  7. A circular ring of radius 3 cm hangs horizontally from a point 4 cm ve...

    Text Solution

    |

  8. The distance between two parallel lines is unity. A point P lies betwe...

    Text Solution

    |

  9. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

    Text Solution

    |

  10. If A+B+C=(3pi)/2, t h e ncos2A+cos2B+cos2C is equal to 1-4cos Acos Bc...

    Text Solution

    |

  11. If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta), then

    Text Solution

    |

  12. In any triangle A B C ,sin^2A-sin^2B+sin^2C is always equal to 2sinAsi...

    Text Solution

    |

  13. The value of sum(r=0)^(10)cos^3(rpi)/3 is equal to 1/4 (b) 1/8 (c) -...

    Text Solution

    |

  14. In triangle ABC,(sinA+sinB+sinC)/(sinA+sinB-sinC) is equal to

    Text Solution

    |

  15. (sin2A+sin2B+sin2C)/(sinA+sinB +sinC) is equal to

    Text Solution

    |

  16. If cos^(2)A+cos^(2)B+cos^(2)C=1, then triangle ABC is

    Text Solution

    |

  17. In a triangle tan A+ tan B + tan C=6 and tan A tan B= 2, then the valu...

    Text Solution

    |

  18. If cos x+cos y-cos(x+y)=(3)/(2), then

    Text Solution

    |

  19. If a sin x+b cos(x+theta)+b cos(x-theta)=d, then the minimum value of ...

    Text Solution

    |

  20. If u=sqrt(a^2 cos^2 theta + b^2sin^2theta)+sqrt(a^2 sin^2 theta + b^2 ...

    Text Solution

    |