Buktikan identitas trigonometri berikut! (sin x)/(1 + cos x) + (1 + cos x)/(sin x) = 2 cosec x

Jawaban yang benar adalah terbukti bahwa (sin x)/(1 + cos x) + (1 + cos x)/(sin x) = 2 cosec x. Ingat! 1/sin x = cosec x sin² x + cos² x = 1 Akan dibuktikan (sin x)/(1 + cos x) + (1 + cos x)/(sin x) = 2 cosec x Perhatikan (sin x)/(1 + cos x) + (1 + cos x)/(sin x) = (sin² x + (1 + cos x)²)/((1 + cos x) sin x) = (sin² x + 1 + 2 cos x + cos² x)/((1 + cos x) sin x) = (sin² x + cos² x + 1 + 2 cos x)/((1 + cos x) sin x) = (1 + 1 + 2 cos x)/((1 + cos x) sin x) = (2 + 2 cos x)/((1 + cos x) sin x) = (2(1 + cos x))/((1 + cos x) sin x) = 2/sin x = 2 cosec x Jadi, terbukti bahwa (sin x)/(1 + cos x) + (1 + cos x)/(sin x) = 2 cosec x.