Dalam segitiga ABC lancip, diketahui sin B = 4/5, hitung cos 1/2 (a+c)

jawab
A+B+C = 180
A+C = 180- B

sin B = 4/5
cos B  = 3/5
cos B = 2 cos² 1/2 B - 1
2 cos² 1/2 B = cos B + 1
cos² 1/2 B = 1/2 cos B + 1/2
cos 1/2 B = √(1/2 cos B + 1/2) = √(1/2 (3/5) + 1/2)
cos 1/2 B = √(3/10 +1/2) = √(4/5) = 2/5 √5

cos 1/2 (A+C) = cos 1/2 (180 - B) = cos 1/2 B
= 2/5 √5