✔ 最佳答案
tan 89 = tan (90 - 1) = 1/tan 1.
so tan 1 x tan 89 = 1............. tan 44 x tan 46 = tan 44 x tan (90 -46) =
tan 44 x 1/tan 44 = 1.
So the numerator = 1 x 1 x ........ x 1 x tan 45 = 1.
cos ^2 89 = cos ^2(90 -1) = sin ^2 1
so cos ^2 1 + cos ^2 89 = cos ^2 1 + sin^2 1 = 1.
cos ^2 44 + cos ^2 46 = cos ^2 44 + cos ^2(90 - 46) = cos ^2 44 + sin ^2 44 = 1
So the denominator = 1 x 44 + cos ^2 45 = 44 + 1/2 = 89/2.
so the answer is 1/(89/2) = 2/89.
2009-03-19 18:55:18 補充：
Correction : Line 2 tan 46 should be = tan (90 - 44) = 1/tan 44. Line 7 cos^2 46 should be = cos^2(90 - 44) = sin^2 44.
