Home
Class 10
MATHS
The value of tan1^@tan2^@tan3^@...tan89^...

The value of `tan1^@tan2^@tan3^@...tan89^@` is

A

`0`

B

`1`

C

`2`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`tan1^(@).tan2^(@).tan3^(@)…….tan89^(@)`
`=tan1^(@).tan2^(@).tan3^(@)….tan44^(@).tan45^(@).tan46^(@)….tan87^(@).tan88^(@).tan89^(@)`
=`tan1^(@).tan2^(@).tan3^(@)…..tan44^(@).(1). Cot 44^(@)……cot3^(@).cot2^(@).cot1^(@)`
`[therefore tan(90^(@)-theta)=cot theta]`
`=tan1^(@).tan2^(@).tan3^(@).....tan44^(@) xx 1/(tan44^(@))...1/(tan30^(@)).1/(tan2^(@)).1/(tan1^(@))` `[therefore cottheta=1/(tantheta)]`
=1
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    NCERT EXEMPLAR|Exercise Coordinate Geometry|58 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    NCERT EXEMPLAR|Exercise Exercise 3.3 Short Answer Type Questions|2 Videos

Similar Questions

Explore conceptually related problems

Value of (tan 1^@ tan2^@ tan3^@...tan89^@) is :

The value of tan1^(0)tan2^(0)tan3^(@)tan89^(@) is 0b.1 c.1/2d .not defined

Find the value of tan 1^@ tan 2^@ tan 3^@ ….tan 45^@ …..tan 88^@ tan 89^@

tan 1^@ tan2^@...tan 89^@=

What is the value of tan 1^(@) tan 2^(@) tan 3^(@) .......... tan 89^(@) ?

The value of tan1^(@)tan46^(@)-tan46^(@)+tan1^(@) is equal to

The value of (tan 1^(@) tan 2^(@) tan 3^(@) … tan 89^(@) ) is

NCERT EXEMPLAR-INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS-Introduction To Trigonometry And Its Applications
  1. If sintheta=a/b, then costheta is equal to

    Text Solution

    |

  2. If cos(alpha + beta)=0, then sin(alpha-beta) can be reduced to

    Text Solution

    |

  3. The value of tan1^@tan2^@tan3^@...tan89^@ is

    Text Solution

    |

  4. If cos9alpha=sinalpha and 9alpha lt 90^(@), then the value of tan5alph...

    Text Solution

    |

  5. If DeltaABC is right angled at C, then the value of cos(A+B) is

    Text Solution

    |

  6. If sinA+sin^2A=1, then the value of cos^2A+cos^4A is

    Text Solution

    |

  7. If sinalpha=1/2 and cosbeta=1/2, then the value of (alpha+beta) is

    Text Solution

    |

  8. Find the value of [(sin^2 2 2^(@)+sin^2 6 8^(@))/(cos^2 2 2^(@)+cos^2 ...

    Text Solution

    |

  9. If 4 tantheta=3, then ((4sintheta-costheta)/(4 sintheta+costheta)) is ...

    Text Solution

    |

  10. if sintheta-costheta=0, then the value of (sin^4theta+cos^4theta)

    Text Solution

    |

  11. Find the value of sin (45^@+theta)-cos (45^@-theta)

    Text Solution

    |

  12. A pole 6 m high casts a shadow 2sqrt 3 m long on the ground, then find...

    Text Solution

    |

  13. value of (tan47^(@))/(cot 43^(@))=

    Text Solution

    |

  14. The value of the expression (cos^(2)23^(@)-sin^(2)67^(@)) is

    Text Solution

    |

  15. The value of the expression (sin80^(@)-cos80^(@)) is negative.

    Text Solution

    |

  16. sqrt((1-cos^(2)theta)sec^(2)theta)=tan theta

    Text Solution

    |

  17. If cosA+cos^2A=1 , then sin^2A+sin^4A= -1 (b) 0 (c) 1 (d) None of ...

    Text Solution

    |

  18. (tantheta+2)(2 tantheta+1)= ?

    Text Solution

    |

  19. If the length of the shadow of a tower is increasing, then the angle o...

    Text Solution

    |

  20. If a man standing on a platform 3 m above the surface of a lake observ...

    Text Solution

    |