buktikan identitas trigonometri berikut 5+4 tan² alfa= 1+4sec²alfa
Matematika
kamyandara
Pertanyaan
buktikan identitas trigonometri berikut
5+4 tan² alfa= 1+4sec²alfa
5+4 tan² alfa= 1+4sec²alfa
1 Jawaban
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1. Jawaban arsetpopeye
5 + 4 tan^2 a
= 5 + 4 (sin^2 a)/(cos^2 a)
= (5 cos^2 a + 4 sin^2 a)/(cos^2 a)
= (cos^2 a + 4 cos^2 a + 4 sin^2 a)/(cos^2 a)
= (cos^2 a + 4(sin^2 a + cos^2 a)) / (cos^2 a)
= (cos^2 a + 4 (1))/(cos^2 a)
= (cos^2 a)/(cos^2 a) + 4/(cos^2 a)
= 1 + 4 sec^2 a