Buktikan bahwa (cos x + cos y)^2 + (sin x + sin y)^2 = 2(1 + cos(x - y))
Matematika
fadhilahalwy
Pertanyaan
Buktikan bahwa
(cos x + cos y)^2 + (sin x + sin y)^2 = 2(1 + cos(x - y))
(cos x + cos y)^2 + (sin x + sin y)^2 = 2(1 + cos(x - y))
1 Jawaban
-
1. Jawaban SadonoSukirno
(cos x + cos y)² + (sin x + sin y)²
= cos²x + cos²y + 2.cos x.cos y + sin²x + sin²y + 2.sin x.sin y
= cos²x + sin²x + cos²y + sin²y + 2(cos x.cos y + sin x.sin y)
= 1 + 1 + 2.cos (x-y)
= 2 + 2.cos (x-y)
= 2(1 + cos (x-y))