Nilai dari (sin 135° ⋅ cos 330° − cos 315° ⋅ sin 150°)/(1 + tan² 240°) = ….

Jawaban yang benar adalah 1/16 (√6 − √2). Pembahasan : Konsep : • sin (180° - x) = sin x • cos (360° - x) = cos x • cos (360° - x) = cos x • sin (180° - x) = sin x • tan (180° + x) = tan x sin 135° = sin (180° - 45°) = sin 45° = 1/2 √2 cos 330° = cos (360° - 30°) = cos 30° = 1/2 √3 cos 315° = cos (360° - 45°) = cos 45° = 1/2 √2 sin 150° = sin (180° - 30°) = sin 30° = 1/2 tan 240° = tan (180° + 60°) = tan 60° = √3 tan² 240° = (tan 240°)² = ( √3)² = 3 (sin 135° ⋅ cos 330° − cos 315° ⋅ sin 150°) / (1 + tan² 240°) = (1/2 √2 ⋅ 1/2 √3 − 1/2 √2 ⋅ 1/2) / (1 + 3) = (1/4 √6 − 1/4 √2) / 4 = 1/4 (√6 − √2) / 4 = 1/16 (√6 − √2) Jadi, (sin 135° ⋅ cos 330° − cos 315° ⋅ sin 150°) / (1 + tan² 240°) = 1/16 (√6 − √2). Semoga membantu ya.