Buktikan bahwa sec×-cos×=sin×.tan!
Jawaban:
sec x – cos x = Sin x. Tan x
pembuktian sisi kiri
sec x – cos x = Sin x. Tan x
1/cos x – cos x = Sin x. Tan x
1- cos²x/ cos x = Sin x. Tan x
( 1-cos²x = sin²x)
sin²x/cos x = Sin x. Tan x
Sin x. sin x/cos x = Sin x. Tan x
(Sin x/ cos x = Tan X)
Sin x. Tan x = Sin x. Tan x (TERBUKTI)
Pembuktian sisi kanan
sec x – cos x = Sin x. Tan x
sec x – cos x = Sin x. Sin x/ cos x
sec x – cos x = sin²x/cos x ……….. (sin²x = 1-cos²x)
sec x – cos x = 1-cos²x/cos x
sec x – cos x = 1/cos x – cos²x/cos x ……..(1/cos x = sec x)
sec x – cos x = sec x – cos x (TERBUKTI)
Penjelasan dengan langkah-langkah:
sec x – cos x = sin x .tan x
sec x – cos x = sinx . sin x/cos x
sec x – cos x = sin²x . 1/cos x
ingat :
- sin²x + cos²x = 1
sin²x = 1 – cos²x
- 1/cos x = sec x
maka
sec x – cos x = sin²x . 1/cos x
sec x – cos x = (1 – cos²x)/ cos x
sec x – cos x = 1 / cos x – cos²x/cos x
sec x – cos x = sec x – cos x
TERBUKTI