Interesting Maths Q9a (Easy)
2011-11-27 7:49 pm
Simplify
[(cosx+1)(cosx-1)]/[(sinx+1)(sinx-1)]+2+[(sinx+1)(sinx-1)]/[(cosx+1)(cosx-1)]
回答 (1)
2011-11-27 9:12 pm
✔ 最佳答案
(cosx + 1) (cosx - 1) / [(sinx + 1) (sinx - 1)] + 2 + (sinx + 1) (sinx - 1) / [(cosx + 1) (cosx - 1)]
= (cos² x - 1) / (sin² x - 1) + 2 + (sin² x - 1) / (cos² x - 1)= (- sin² x) / (- cos² x) + 1 + (- cos² x) / (- sin² x) + 1= 1 / cos² x + 1 / sin² x= 1 / (sin x cos x)²= 1 / ( (1/2) sin 2x )²= 4 csc² 2x
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https://hk.answers.yahoo.com/question/index?qid=20111127000051KK00225