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(1+sin4a-cos4a)/(1+sin4a+cos4a)=?
题目详情
▼优质解答
答案和解析
(1 + sin 4 a - cos 4 a) / (1 + sin 4 a + cos 4 a)
= (1 - cos 4 a + sin 4 a) / (1 + cos 4 a + sin 4 a)
= (2 sin^2 2 a + 2 sin 2 a cos 2 a)/ (2 cos^2 2 a + 2 sin 2 a cos 2 a)
= [2 (sin 2 a) (sin 2 a + cos 2 a)]/ [2 (cos 2 a) (cos 2 a + sin 2 a)]
= sin 2 a / cos 2 a
= tan 2 a .
= (1 - cos 4 a + sin 4 a) / (1 + cos 4 a + sin 4 a)
= (2 sin^2 2 a + 2 sin 2 a cos 2 a)/ (2 cos^2 2 a + 2 sin 2 a cos 2 a)
= [2 (sin 2 a) (sin 2 a + cos 2 a)]/ [2 (cos 2 a) (cos 2 a + sin 2 a)]
= sin 2 a / cos 2 a
= tan 2 a .
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