Bang popeye Buktikan bahwa: Tg a - cot a ------------------ = 2 sin ^2 a -1 Tg a + cot a

Bab Trigonometri
Matematika SMA Kelas X

(Tan a - cot a)/(tan a + cot a)
= (tan a - 1/tan a) / (tan a + 1/tan a)
= (tan² a - 1)/tan a : (tan² a + 1)/tan a
= (tan² a - 1)/(tan² a + 1)
= (tan² a - 1)/sec² a
= (sin² a/cos² a - 1) . cos² a
= sin² a - cos² a
= - (cos² a - sin² a)
= - (cos 2a)
= - (1 - 2 sin² a)
= 2 sin² a - 1

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