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![[Post New]](/templates/default/images/icon_minipost_new.gif) 21 Mar 2008 09:23:25 IST
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evaluate
tan9 - tan27 - tan63 + tan81
i am getting answer as 0 but given answer is 4
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adversities cause some men to break other to break records............i m of the other type....... :-) |
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21 Mar 2008 12:04:33 IST
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![[tex] \\ \\ (\tan9+\tan81) - (\tan27+\tan63) \\ \\ (\tan9+\frac{1}{\tan9}) - (\tan27+\frac{1}{\tan27}) \\ \\ (\frac{\sec^29}{\tan9}) - (\frac{\sec^227}{\tan27}) \\ \\ \frac{\sec^29}{\tan9} = \frac{1}{\sin9 \cos9} = \frac{2}{\sin18} , \frac{\sec^227}{\tan27} = \frac{1}{\sin27 \cos27} = \frac{2}{\sin54} \\ \\ (\frac{2}{\sin18}) - (\frac{2}{\sin54}) \\ \\ \sin18 = \frac{\sqrt{5} - 1}{4} , \sin54 = \frac{\sqrt{5} + 1}{4} \\ \\ \frac{8}{\sqrt{5} - 1} - \frac{8}{\sqrt{5}+1} = \frac{16}{4} = 4](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/d/f/0df2242ad2ec936be3bd3340241e3e19bfc9ca12.gif)
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this reply: 14 points
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21 Mar 2008 13:34:50 IST
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Just a continuation of sboosy's post without making use of values of  and  . |
Guide to latex:
http://www.goiit.com/posts/list/community-shelf-a-guide-to-latex-48056.htm
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this reply: 10 points
(with 2
in 2 votes ) [?]
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