Cos x per 1+ sin x + 1+ sin x per cos X
Matematika
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Pertanyaan
Cos x per 1+ sin x + 1+ sin x per cos X
1 Jawaban
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1. Jawaban bapakdr
(cos x / 1+sin x) + (1+sin x / cos x)
jadi jika a/b + b/a = (a² + b²)/ba
(cos²x + 1 + 2sin x + sin²x) / cos x(1+sin x)
= (cos²x+sin²+1+2.sin x) / cos x(1+sin x)
= (1 + 1 + 2.sin x) / cos x(1 + sin x)
= (2 + 2.sin x) / cos x(1 + sin x)
= 2(1 + sin x) / cos x(1 + sin x)
= 2 / cos x
= 2 (1 / cos x)
= 2 sec x