IIT JEE , AIEEE Forum - Mathematics , Trignometry

hsbhatt

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).

mukulss

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.......

konichiwa2x

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

hsbhatt

So, who do you think set the paper?

rockey

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

hsbhatt

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

rockey

sorry A+B=45 for above one

konichiwa2x

dont tell me u work in fiitjee..

hsbhatt

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

konichiwa2x

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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