Buktikan kesetaraan identitas trigonometri berikut!
Buktikan kesetaraan identitas trigonometri berikut!
cot² x - cos² x = cot² x. cos² x
ruas kiri
cot² x - cos² x =
[tex]\sf = \dfrac{cos^2\ x}{sin^2\ x}- cos^2 \ x[/tex]
[tex]\sf = \dfrac{cos^2\ x - cos^2 \ x. sin^2\ x}{sin^2 \ x}[/tex]
faktorkan
[tex]\sf = \dfrac{cos^2\ x (1-sin^2\ x)}{sin^2 \ x}[/tex]
[tex]\sf = \dfrac{cos^2\ x \ . (cos^2\ x)}{sin^2 \ x}[/tex]
[tex]\sf = \dfrac{cos^2\ x}{sin^2\ x}. (cos^2\ x)[/tex]
[tex]\sf = cot^2 \ x . cos^2\ x \to terbukti \ sama \ dengan \ ruas\ kanan[/tex]
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