Question

Kak, tolong bantu saya dong menjawab nomor 12 dengan penyelesaian.........
besok dikumpul nih......

Answer 1

Verified answer

Segitiga ABC

∠A = ∠C = 45°

AB = BC = a

AC = a√2

AK = √(AB² + BK²) = √(a² + (1/2 a)²)

AK = 1/2 a√5

AK/sin C = KC/sin x

1/2 a√5 / 1/2 √2 = 1/2 a / sin x

sin x = 1/2 × √2 / √5

sin x = 1/10 √10

sin x = 1/√10

cos x = √(1 - sin² x)

cos x = √((10 - 1)/10)

cos x = 3/√10

sin 2x = 2 sin x cos x = 6/10 = 3/5

cos 2x = 1 - 2 sin² x = 1 - 2/10 = 4/5

sin 3x

= sin (2x + x)

= sin 2x cos x + cos 2x sin x

= 3/5 × 3/√10 + 4/5 × 1/√10

= 13/(5√10)

sin 2x + sin 3x

= 3/5 + 13/5√10

= (3√10 + 13)/5√10

= (3√10 + 13)√10 / 50

= (30 + 13√10)/50