prove that
(1+sin x +cos x)/(1+sin x-cos x) = cosec x (1+cos x)
mathz trigonometric function
2010-09-21 2:55 am
回答 (1)
2010-09-21 3:09 am
✔ 最佳答案
(1+sin x +cos x)/(1+sin x-cos x)= (1 + sin x + cos x)² / (1+sin x-cos x)(1 + sin x + cos x)= (1 + 2(sinx + cosx) + 1 + 2sinx cosx) / [(1 + sin x)² - cos² x]= 2(1 + sinx + cosx + sinx cosx) / (sin² x + 2sin x + 1 - cos² x)= 2(1 + sinx + cosx + sinx cosx) / (sin² x + 2sin x + sin² x)= 2(sinx + 1)(cosx + 1) / [(2sin x) (sin x + 1)]= (cos x + 1) / sin x= cosec x (1+cos x)
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