hitunglah [tex] \frac{ \sin(90) }{ \cos(105) } [/tex]

Kelas 10 Matematika
Bab Trigonometri

sin 90° / cos 105°
= 1 / (cos (60° + 45°))
= 1 / (cos 60° . cos 45° - sin 60° . sin 45°)
= 1 / (1/2 . 1/2 √2 - 1/2 √3 . 1/2 √2)
= 1 / (1/4 √2 - 1/4 √6)
= 1 / (1/4 . (√2 - √6))
= 4 / (√2 - √6)
= (4/(√2 - √6)) . ((√2 + √6)/(√2 + √6))
= (4 (√2 + √6)) / (√2² - √6²)
= (4 (√2 + √6)) / (2 - 6)
= (4 (√2 + √6)) / (-4)
= -√2 - √6