sederhanakanlah cos x / 1+sin x + 1+sin x / cos x
Matematika
ninisase
Pertanyaan
sederhanakanlah
cos x / 1+sin x + 1+sin x / cos x
cos x / 1+sin x + 1+sin x / cos x
1 Jawaban
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1. Jawaban Robinn
cosx / 1+sinx + 1+sinx / cosx
= cosx + (1 + sinx)(1 + sinx) / cosx(1 + sinx)
= cosx + (1 + sinx)² / cosx (1 + sinx)
= cos²x + 1 + 2sinx + sin²x / cosx(1+sinx)
= 2 + 2 sinx / cosx (1 + sinx)
= 2 (1 + sinx) / cosx (1 + sinx)
= 2 (1 / cosx)
= 2secx