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I need to show two auxiliary trigonometric identities:

1) $\sec^2x = \tan ^2x + 1 (\cos x \neq 0)$

2) $\csc^2x = \cot^2x +1 (\sin x \neq 0)$

How could I do it?


[Original Portuguese]

Identidades Trigonométricas Auxiliares Sendo preciso mostrar a demonstração das duas fórmulas das IDENTIDADES TRIGONOMÉTRICAS AUXILIARES:

1) sec²x = tg²x + 1 (cos x ≠ 0)

2) cossec²x = cotg²x = 1 (sen x ≠ 0)

Como seria possível fazê-lo???

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    Welcome! It will be nice if you write in English .2012-09-11
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    @Iuli [Consensus on meta in the past](http://meta.math.stackexchange.com/questions/1617/what-is-the-site-etiquette-about-i-asking-and-ii-answering-questions-in-a-la) has been very strongly in favor of people posting questions in their native languages. The idea that it is much better to get a coherent, well-expressed question in Portuguese, and which can be translated, than to get an unintelligible question in English.2012-09-11
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    @ MJD: I translated the question to English already, it's just that the OP has not yet accepted the edit.2012-09-11
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    @RodCarvalho Are you sure? I would expect that your edit would go into the queue to be approved by high-reputation users, not by OP. But it is not in the queue.2012-09-11
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    @ MJD: It said it was sent to the queue after I submitted the edit. In any case, Peter translated it in the meantime.2012-09-11
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    I think in such cases it might be a good idea to leave the original language in the post, to facilitate correction of translation errors.2012-09-11
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    OH!! Sorry for the inconvenience, but I'm brazilian and I cannot express my question very well in English; But I'm so gratify for the answers. Really thanks, you were my salvation. Haha...2012-09-11
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    @Ana It is OK to post in Portuguese.2012-09-11

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