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Trignometry

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18 Jan 2008 09:39:30 IST

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Trigonometry

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Find the value of (1+tan1) (1+tan2) (1+tan3) ... (1+tan 45). here the numbers are degrees i.e. tan 1 means tan(1 degree).

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mukul bansal

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Joined: 9 Sep 2007

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18 Jan 2008 11:19:48 IST

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i think this is a good que.....

1+ tan 1 = 1 + tan(45-44)
= 1 + 1-tan44
---------
1+ tan44

= 2/(1+ tan 44)

and it will get canceled out with (1+ tan 44) leaving a remainder of 2...

in this way u will finally cancel out (1+ tan 22) and (1+ tan 23)

leaving with u:

2^22 *(1+ tan 45)

finally u get:

2^23

hope u got it now.......

Abhijith

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11 Feb 2008 18:43:07 IST

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this question came in the open test yersterday! whats the source?

Hari Shankar

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11 Feb 2008 18:55:27 IST

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So, who do you think set the paper?

rockey

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11 Feb 2008 19:00:40 IST

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it is 2^23.
(tan A+1)(tan B+1) =2 if A+B =45
hope u like it

Hari Shankar

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11 Feb 2008 19:06:06 IST

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rocky, i think you meant A+B = 45^o. Yeah you've got it.

rockey

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11 Feb 2008 19:06:55 IST

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sorry A+B=45 for above one

Abhijith

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11 Feb 2008 21:00:40 IST

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dont tell me u work in fiitjee..

Hari Shankar

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11 Feb 2008 21:21:02 IST

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i was joking man. i found it in a book called 103 Trigonometry Problems by Titu Andreescu and Zuming Feng under Introductory Problems. Nice book, but under Advanced Problems you find some beasty problems which only IMO guys find exciting

Abhijith

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11 Feb 2008 21:48:07 IST

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oh allright..anyway thanks to u, I didnt even how to do that problem. I remember the answer.

In fact goiit is becoming quite famous. There were 3 questions in the test yesterday that were discussed in our forums.

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