Question

Nilai dari 4 sin 75⁰ sin 15⁰ adalah…
a. √2
b. √3
c. 1/2 √2
d. (-1)/2 √2
e. -3√2
Pakai cara yg bener yaaa..

Answer 1

4 sin 75 sin 15
= -2 . -2 sin 75 sin 15
= -2 (cos (75+15) - cos (75-15))
= -2 (cos 90 - cos 60)
= -2(0 - 1/2)
= 1

Answer 2

4 . sin 75 . sin 15 = 4 . sin (45+30) . sin (45-30)
= 4 . (sin 45.cos 30 + cos 45.sin30) . (sin 45.cos 30 - cos 45.sin 30)
= 4 . (1/2 √2 . 1/2 √3 + 1/2 √2 . 1/2) . (1/2 √2 . 1/2 √3 - 1/2 √2 . 1/2)
= 4 . (1/4 √6 + 1/4 √2) . (1/4 √6 - 1/4 √2)
= 4 . ((1/4 √6)² - (1/4 √2)²)
= 4 . (6/16 - 2/16)
= 4 . (4/16)
= 4 . 1/4
= 1