Nilai tan 105° adalah.... [tex]a. \: (2 + \sqrt{3)} [/tex] [tex]b. \: (2 - \sqrt{3)} [/tex] [tex]c. \: - (2 + \sqrt{3)} [/tex] [tex]d. \: - (3 + \sqrt{3)

Kelas 11 Matematika
Bab Trigonometri Lanjut

tan 105°
= tan (45° + 60°)
= (tan 45° + tan 60°)/(1 - tan 45° . tan 60°)
= (1 + √3)/(1 - 1 . √3)
= (1 + √3)/(1 - √3)
= ((1 + √3)/(1 - √3)) . ((1 + √3)/(1 + √3))
= (1 + √3)²/(1² - √3²)
= (1 + 2 . 1 . √3 + √3²)/(1 - 3)
= (1 + 2√3 + 3)/(-2)
= (4 + 2√3)/(-2)
= - (2 + √3)