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I was stumped by another past-year question:

In $\triangle ABC$, prove that $$\cot(A)\cot(B)+\cot(B)\cot(C)+\cot(C)\cot(A)=1.$$

Here's what I have done so far: I tried to replace $C$, using $C=180^\circ-(A+B)$. But after doing this, I don't know how to continue.

I would be really grateful for some help on this, thanks!

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    It would be better if u showed what have you tried or what are your ideas as to begin with a solution for this.2011-09-07
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    @Sophia Please post questions showing that you have put some effort into trying to solve the problem. By the way are you posting this question in preparation for your SPM?2011-09-07
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    @D B Lim: Nope, I am only doing them for my school's final examination. I will only have my SPM next year. As for showing effort, I have been thinking, asking friends, looking up info about the topic, but still don't know how to continue.2011-09-07
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    What they meant was that you show what algebra you've tried to solve this problem (i.e., what you've tried writing on paper).2011-09-07
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    Not an answer, but you might have seen the identity: $\tan A + \tan B + \tan C = \tan A \cdot \tan B \cdot \tan C$. These two are really the same.2011-09-07
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    @Sophia Do you do mathematics to get high grades or do you like the subject?2011-09-07
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    @D B Lim Neither, I am just doing my duty as a student, and learn as much as possible!2011-09-21

3 Answers 3