Identify the expression that completes the equation so that it is an identity.
Cos x / 1+sin x = ?
Options:
A.) 1-sin x/cos x
B.) sin x
C.) 1+sec x / sec x
D.) 1+csc x / csc x
Confused?? :(?
2017-03-28 12:42 am
回答 (2)
2017-03-28 12:48 am
cos x / (1 + sin x)
= cos x (1 - sin x) / [(1 + sin x) (1 - sin x)]
= cos x (1 - sin x) / (1² - sin²x)
= cos x (1 - sin x) / (1 - sin²x)
= cos x (1 - sin x) / (sin²x + cos²x - sin²x)
= cos x (1 - sin x) / cos²x
= (1 - sin x) / cos x
The answer: A.) (1 - sin x) / cos x
= cos x (1 - sin x) / [(1 + sin x) (1 - sin x)]
= cos x (1 - sin x) / (1² - sin²x)
= cos x (1 - sin x) / (1 - sin²x)
= cos x (1 - sin x) / (sin²x + cos²x - sin²x)
= cos x (1 - sin x) / cos²x
= (1 - sin x) / cos x
The answer: A.) (1 - sin x) / cos x
2017-03-28 12:42 am
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收錄日期: 2021-04-20 19:36:33
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