Cos x / 1-tan x + sin x / 1 - cot x = A.0 B.1 C.sin x + cos x D.Cos x - sin x E. Tan x
Matematika
gepe
Pertanyaan
Cos x / 1-tan x + sin x / 1 - cot x =
A.0
B.1
C.sin x + cos x
D.Cos x - sin x
E. Tan x
A.0
B.1
C.sin x + cos x
D.Cos x - sin x
E. Tan x
1 Jawaban
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1. Jawaban Enrico08
cos x /(1 - tan x) + sin x/(1 - cot x)
= cos x/(1 - sin x/cos x) + sin x/(1 - cos x/sin x)
= (cos^2 x)/(cos x - sin x) + (sin^2 x)/(sin x - cos x)
= -(cos^2 x)/(sin x - cos x) + (sin^2 x)/(sin x - cos x)
= (sin^2 x - cos^2 x)/sin x - cos x
= (sin x + cos x)(sin x - cos x)/sin x - cos x
= sin x + cos x (C)