Kenapa tan α = √(sec²α - 1) ?

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Berdasarkan Identitas Trigonometri
Sec² a - Tan² a = 1
Sec² a - 1 = Tan²a
Tan² a = Sec²a - 1
Tan a = √[Sec²a - 1]

Berdasarkan identitas trigonometri:
sin²a + cos²a = 1
(sin²a + cos²a) ÷ cos²a = 1 ÷ cos²a
[tex] \frac{sin^{2} a}{cos^{2}a } + \frac{cos^{2}a }{cos ^{2} a} = \frac{1}{cos ^{2} a} \\tan ^{2}a+1=sec ^{2}a\\tan ^{2}a=sec ^{2}a-1\\ [/tex]
(tan a)² = sec²a - 1
tan a = √(sec²a - 1)