tan 2 x/sec x-1 -1 = secx

tan 2 x/sec x-1 -1 = secx

Identitas Trigonometri
tan x = sin x / cos x
sec x = 1/cos x
sec² x – 1 = tan² x

Akan dibuktikan :
(tan² x /(sec x – 1)) – 1 = sec x

(tan² x /(sec x – 1)) – 1
pembilang dan penyebut kalikan (sec x + 1)
= (tan² x (sec x + 1) / (sec x – 1)(sec x + 1)) – 1
= (tan² x (sec x + 1) / (sec² x – 1)) – 1
= (tan² x (sec x + 1) / tan² x) – 1
= sec x + 1 – 1
= sec x
terbukti