Question

Buktikan identitas-identitas berikut:
(1+cos^2 x)(1+cot^2 x) =1

Answer 1

Itu mungkin maksud soalnya (1 - cos^2 x)(1+cot^2 x) =1
(1 - cos^2 x)(1 + (cosx/sinx)^2) = 1
(1 - cos^2 x)(1 + (cos^2 x /sin^2 x)) = 1
(1 - cos^2 x)((sin^2 x + cos^2 x)/sin^2 x) = 1
(1 - cos^2 x)(1/sin^2 x) = 1
Ingat bahwa sin^2 x + cos^2 x = 1
cos^2 x = 1 - sin^2 x, maka
(1 - cos^2 x)/(1 - cos^2 x) = 1 (terbukti).

Tapi kalau soalnya

(1 + cos^2 x)(1 + (cosx/sinx)^2) = 1
(1 + cos^2 x)(1 + (cos^2 x /sin^2 x)) = 1
(1 + cos^2 x)((sin^2 x + cos^2 x)/sin^2 x) = 1
(1 + cos^2 x)(1/sin^2 x) = 1
Ingat bahwa sin^2 x + cos^2 x = 1
cos^2 x = 1 - sin^2 x, maka
(1 +cos^2 x)/(1 - cos^2 x) = 1 (Tidak terbukti).

semoga membantu :)