(1 + sin x / cos x) + (cos x / 1 + sin x)
Matematika
surati2
Pertanyaan
(1 + sin x / cos x) + (cos x / 1 + sin x)
2 Jawaban
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1. Jawaban DB45
Bentuk sederhana dari
(1+sin x)/ cos x + (cos x)/ (1 +sin x) =
= {(1+sin x)(1+sin x) + cos x (cos x)} / ( cos x )(1+ sin x)
= (1 + 2 sin x + sin² x + cos² x) / cos x(1+sin x)
= (1 + 2 sin x + 1 ) / 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 sec x -
2. Jawaban arsetpopeye
(1 + sin x)/(cos x) + (cos x)/(1 + sin x) . (1 - sin x)/(1 - sin x)
= (1 + sin x)/(cos x) + (cos x(1 - sin x))/(1 - sin^2 x)
= (1 + sin x)/(cos x) + (cos x(1 - sin x))/(cos^2 x)
= (1 + sin x)/(cos x) + (1 - sin x)/(cos x)
= (1 + sin x + 1 - sin x) / (cos x)
= 2 / cos x
= 2 sec x