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I'm not sure if:
Is the complete problem. Can you double check it?

19 December 2011

yeah its supposed to simplify to sec^2(x)

20 December 2011

Bec

21 December 2011

To solve this question, you need to trigonometry identity:
(1) cos2(x) + sin2(x) = 1
(2) tan2(x) + 1 = sec2(x)
By using (1), you will realise 1-sin2(x) = cos2(x), so the fraction cancels itself!
1-sin2(x)/cos2(x) = cos2(x)/cos2(x) = 1
Then you are left with:
1+tan2(x)
Which is sec2(x) because of (2)
Note that (2) can be derived from (1) by dividing the whole equation by cos2(x)
cos2(x)/cos2(x) +sin2(x)/cos2(x) = 1/cos2(x)
1+tan2(x) = sec2(x)

21 December 2011

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