Problem 3
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Started by: Baba001Baba001
On: 1208282338|%e %b %Y, %H:%M %Z|agohover
Number of posts: 4
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Crack this!!
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Problem 3
Baba001Baba001 1208282338|%e %b %Y, %H:%M %Z|agohover

\tan 15 \tan 25 \tan 35 = \tan \theta

Solve for \theta.

Looks simple eh?1

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last edited on 1208282408|%e %b %Y, %H:%M %Z|agohover by Baba001 + show more
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Re: Problem 3
sloggerslogger 1208303796|%e %b %Y, %H:%M %Z|agohover

\tan 15 \tan 25 \tan 35 \\ \\ = \frac{\tan 15}{\tan 55 \tan 65} \\ \\ =\frac{\tan 5\tan 15}{\tan 5 \tan (60 - 5) \tan (60 + 5)}\\ \\ \mbox{Using }\tan x \tan(60 - x)\tan (60 + x) = \tan 3x \\ \\ = \frac{\tan 5\tan 15}{\tan 15 }\\ \\ = \tan 5 \\ \\hence \ \theta = 5

last edited on 1208304033|%e %b %Y, %H:%M %Z|agohover by slogger + show more
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Re: Problem 3
madnessweasleymadnessweasley 1208316337|%e %b %Y, %H:%M %Z|agohover

shreyas and chappli can die here. You said that only if you knew the answer to the problem, you could solve it but it seems not :D1

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Re: Problem 3
Baba001Baba001 1208409475|%e %b %Y, %H:%M %Z|agohover

Excellent Solution. Here's what I had in mind.

(1)
Let \theta = 5^o Given Exp: \tan 3\theta \tan(30- \theta) \tan (30 + \theta) On Simplifying, we get Exp = \tan \theta

And so the answer is 5. :D

last edited on 1208409545|%e %b %Y, %H:%M %Z|agohover by Baba001 + show more
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