Home
Class 12
MATHS
Find tan1^0tan2^0......tan89^0...

Find
`tan1^0tan2^0......tan89^0`

Text Solution

Verified by Experts

`L.H.S.=(tan1^@tan89^@)(tan2^@tan88^@)…`
`(tan44^@tan46^@)tan45^@`
`=[tan1^@tan(90^@-1^@)][tan2^@tan(90^@-2^@)]…`
`[tan44^@tan(90^@-44^@)]tan45^@`
`=(tan1^@cot1^@)(tan2^@cot2^@)…`
`(tan44^@cot44^@)tan45^@=1`
`[ :'tanthetacottheta" and " tan45^@=1]`
=R.H.S.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise example|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.1|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

Find the value of log tan1^0logtan2^0...........logtan89^0

Prove that (1+tan1^0)(1+tan2^0)......(1+tan45^0)=2^(23)dot

Prove that tan1^@tan2^@tan3^@...tan88^@tan89^@=1

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

Prove that tan 1^@ tan 2^@ tan 3^@........ tan 88^@tan89^@=1

The value of tan6^0tan42^0tan66^0tan78^0 is (a)1 (b) 1/2 (c) 1/4 (d) 1/8

tan100^0+tan125^0+tan100^0tan125^0 is equal to

Prove that tan20^0tan40^0tan80^0=tan60^0

tan1^(@)tan2^(@)tan3^(@)........................tan89^(@)=

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Find tan1^0tan2^0......tan89^0

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

    Text Solution

    |

  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |