Buktikan identitas trigonometri ini (Tan x + sin x) (1-cos x ) = sin^2 x tan x
Matematika
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Pertanyaan
Buktikan identitas trigonometri ini
(Tan x + sin x) (1-cos x ) = sin^2 x tan x
(Tan x + sin x) (1-cos x ) = sin^2 x tan x
1 Jawaban
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1. Jawaban Anonyme
jawab
(tan x + sin x) (1 - cos x) = sin² x tan x
(tan x + sin x) (1 - cos x) =
= tan x - tan x cos x + sin x - sin x cos x
= sin x/cos x - sin x/cos x . cos x + sin x - sin x cos x
= (sin x/cos x) - (sin x) + (sin x) - sin x cos x
= (sin x/cos x ) - sin x cos x
= (sin x - sin x cos²x)/(cos x)
= sin x (1 - cos² x) /(cos x)
= sin x ( sin² x) /cos x
= (sin² x)(sin x/cos x)
= (sin² x)(tan x)