kak bantu no 42 dong pliss

Bab Trigonometri
Matematika SMA Kelas X

cos 75°
= cos (30° + 45°)
= cos 30° . cos 45° - sin 30° . sin 45°
= 1/2 √3 . 1/2 √2 - 1/2 . 1/2 √2
= 1/4 (√6 - √2)

cos 15°
= cos (45° - 30°)
= cos 45° cos 30° + sin 45° sin 30°
= 1/2 √2 . 1/2 √3 + 1/2 √2 . 1/2
= 1/4 (√6 + √2)

1/cos 75° + 1/cos 15°
= 4/(√6 - √2) + 4/(√6 + √2)
= (4 (√6 + √2) + 4 (√6 - √2))/(√6² - √2²)
= (4√6 + 4√2 + 4√6 - 4√2)/(6 - 2)
= (8√6)/4
= 2√6

✩✩ E ✩✩