cos 75° × sin 15°

Hallo Ahmad, kakak bantu jawab yaaa Jawaban : (2-√3)/4 Ingat kembali: Sin (a-b)=Sin a.Cos b - Cos a. Sin b Cos (a+b)=Cos a . Cos b - Sin a . Sin b Sin 45° = (1/2)√2 Sin 30° = 1/2 Cos 45° = (1/2)√2 Cos 30° = (1/2)√3 (a - b)(a - b) = a.a - 2ab + b.b Pembahasan : cos 75° = Cos (45°+30°), maka --------> = Cos 45° . Cos 30° - Sin 45° . Sin 30° --------> =(1/2)√2 . (1/2)√3 - (1/2)√2 . (1/2) --------> =(1/4)√6 - (1/4)√2 Sin 15° = Sin (45°-30°) --------> =Sin 45°.Cos 30° - Cos 45°. Sin 30° --------> = (1/2)√2 . (1/2)√3 - (1/2)√2 . (1/2) --------> =(1/4)√6 - (1/4)√2, maka cos 75° × sin 15° =((1/4)√6 - (1/4)√2)x ((1/4)√6 - (1/4)√2) -----> =(1/4)√6. (1/4)√6 - (1/4)√6 . (1/4)√2 - (1/4)√2 . (1/4)√6 + (1/4)√2.(1/4)√2 -------------------->= (1/16)√36 - (1/16) √12 - (1/16) √12 + (1/16)√4 -------------------->= (1/16) . 6 - (2/16) √12 + (1/16) . 2 -------------------->= 6/16 - 2/16 √4.3 + 2/16 -------------------->= 6/16 - 2/16 .2√3 + 2/16 -------------------->=6/16 - 4/16 √3 + 2/16 -------------------->=(6+2-4√3 )/16 -------------------->=(8 - 4√3 )/16 -------------------->=(2-√3)/4 ----> pembilang dan penyebut dibagi 4 Jadi, hasil dari cos 75° × sin 15° adalah (2-√3)/4